US President Barack Obama said pressed his Chinese counterpart on trade, currency and human rights during talks at the White House.
Speaking at a joint news conference, Mr Obama said he believed China's "peaceful rise" was good for the US.
Chinese President Hu Jintao described the talks as candid and constructive.
Asked by a reporter to justify China's human rights record, he said China had made "enormous progress" on the issue, but a lot remained to be done.
Earlier, Mr Obama hailed relations with China, saying the two countries have a huge stake in each other's success.
At a White House ceremony to greet Mr Hu, he said the US and China would be more prosperous and secure when they worked together.
Mr Hu said co-operation should be based on mutual respect, and they should respect each other's development paths.
The two leaders' talks at the White House tackled issues from currency and trade to defence and security.
'Frank and candid'
President Obama told the joint news conference that together they had shown what the two nations could do if they co-operated.
"As we look to the future, what's needed is a spirit of co-operation that is also friendly competition," Mr Obama said.
Questioned about how the US viewed China's human rights record, Mr Obama said the leaders had discussed the issues "in a frank and candid way".
The task of the US was to focus on areas of agreement while acknowledging "there are areas where we disagree".
"Thirty years from now we will have seen further evolution and further change," Mr Obama said.
Meanwhile US officials revealed that a $45bn (£28bn) export deal had been signed with China, including Beijing's $19bn purchase of 200 Boeing aircraft.
The BBC's Paul Adams in Washington say the US administration is making sure this state visit lacks none of the required pomp.
After Mr Hu's arrival, the two leaders shook hands as the Chinese leader was welcomed with full military honours.
They stood on the White House lawn as a military band played the two national anthems accompanied by a 21-gun salute, then walked over to meet invited members of the public before addressing the crowds.
"We have an enormous stake in each other's success," Mr Obama said. "We will be more prosperous and more secure when we work together."
He cited President Jimmy Carter's meeting with Chinese leader Deng Xiao Ping in 1979 which normalised relations between the two countries, frozen for the previous 30 years.
He said the current visit would lay the basis for the next 30 years of ties.
He also referred to human rights.
"History shows that societies are more harmonious, nations are more successful and the world is more just, when the rights and responsibilities of all nations and all people are upheld. Including the universal rights of every human being," he said.
In response, Mr Hu said co-operation between the two countries in various fields had produced "fruitful results" and relations had "achieved new progress".
"Our cooperation as partners should be based on mutual respect," he said.
"We live in an increasingly diverse and colourful time. China and the United States should respect each other's choice of development path and each other's core interests. We should deepen mutual understanding through communication, increase mutual trust through dialogue and expand common ground through exchanges."
As the ceremony was going on, on the other side of the White House pro-Tibet demonstrators vented their anger against what they regard as a repressive regime, chanting: "Who is a liar? Hu Jintao is a liar" and "Killer,killer, Hu Jintao."
Mr Hu arrived at Andrews Air Force base outside Washington on Tuesday and was greeted by US Vice-President Joe Biden before attending a private dinner at the White House hosted China and US pledge stronger tiesby President Obama.
As Mr Hu dined, activists outside the White House held aloft banners urging the US president to to "admonish Hu" over China's human rights abuses.
Western TV reports of Mr Hu's trip broadcast in China were blacked out when the crowds of protesters were shown - one BBC report showing footage of human rights protesters demonstrating outside the White House was blacked out for 30 seconds.
The White House is laying on a full formal reception with lunch at the state department, dinner at the White House, and meetings with some of America's most powerful business leaders from firms like General Electric, Coca-cola and Boeing.
"Whether we're dealing with economic discussions, whether we're dealing with those in the security realm, or whether we're doing those with human rights, I think this is an argument that we have and we'll continue to make to the Chinese and push them to do better," spokesman Robert Gibbs told reporters.
The BBC's Damian Grammaticas in Beijing says the US wants a co-operative relationship, but is starting to talk tougher over Beijing's management of its exchange rate and its support for the regime in North Korea.
This is likely to be Mr Hu's last state visit to the US before a handover of power is completed in China in 2013.
US Secretary of State Hillary Clinton said America and China were "at a critical juncture to determine how good the co-operative relationship between our two countries can be".
"I believe that the Chinese and American governments and people need to work together towards solving problems in a win-win way," Mrs Clinton told China's CCTV.
As the world's two biggest economies, she said, China and the US shared special responsibilities over such issues as the threat to world stability posed by nuclear programmes in Iran and North Korea, and the need for a concerted response to climate change.
"We will continue to have our disagreements but that should not interfere with dealing with these other big issues that we face," added Mrs Clinton.
In a separate interview for the US network ABC, the secretary of state said some Chinese "entities" were not complying with UN sanctions against Iran over its nuclear programme, and that the US was pushing Beijing very hard on this issue.
Correspondents say both sides recognise the deep divisions that have strained relations over the past year - the value of the yuan, the huge trade gap, human rights, and US arms sales to Taiwan. The US is also concerned by China's growing military strength.
Later in the week, Mr Hu is expected to travel to Chicago, where some predict he will sign a series of trade and investment agreements.
The US is encouraging China to buy tens of billions of dollars of aircraft, car parts, agricultural goods and beef.
Trade between the US and China is worth $400bn, up from $100m 30 years ago, when the US formalised relations with the communist state.
China also holds the world's largest foreign currency reserves at $2.85tn and a major share of US government debt.