President Barack Obama has pressed for reform of US immigration policy in his first major speech on the issue.
Mr Obama has made immigration reform a priority amid pressure from border states to tackle illegal immigration and drug violence.
He said the US had thrived as a nation of immigrants but reform had been held hostage by "political posturing".
It was possible, he added, to "shape a practical, common-sense approach that reflects our heritage and our values".
He said the country needed one clear national standard but nothing could happen unless Republicans and Democrats worked together in Congress.
The White House said recent developments influenced Mr Obama's decision to make his speech on Thursday.
Arizona recently enacted a law which makes it a crime to be in the state without immigration papers.
In his speech, Mr Obama said the Arizona issue had divided opinion in the US.
"But everywhere people have expressed frustration with a system that seems fundamentally broken," he said.
Mr Obama said US borders had been porous for decades and there were an estimated 11 million undocumented immigrants in the country.
"The majority of Americans are sceptical of a blanket amnesty and they are also sceptical that it is possible to round up and deport 11 million people," he said.
"It would tear at the very fabric of this nation because immigrants who are here illegally are already intricately woven into that fabric."
He said many illegal migrants had children who had been brought up as Americans and who only discovered their illegal status when they applied for college or for a job.
Mr Obama said migrant workers - mostly in the US illegally - had been the labour force for farmers and agricultural producers "for generations".
But he added: "Once we get past the two poles of this debate it is possible to shape a practical common-sense approach that reflects our heritage and our values."
The president said immigration reform could only be achieved if Republicans and Democrats worked together.
"The question now is whether we will have the courage and the political will to pass a bill through Congress, to finally get it done," he said.
"The fact is, that without bipartisan support... we cannot solve this problem. Reform that brings accountability to our immigration system cannot pass without Republican votes.
"The only way to reduce the risk that this effort will again falter because of politics, is if members of both parties are willing to take responsibility for solving this problem once and for all."
Mr Obama delivered his speech at the American University's School of International Service, in Washington.
The BBC's Paul Adams in Washington says that despite his urgent tone, President Obama did not say when he thought Congress should act.
Very few people think movement is likely before November's mid-term elections, he adds.
Arizona's controversial law has already brought a legal challenge from Mexico, which says it could discriminate against its citizens.
At the time, President Obama called the law misguided and has asked the Justice Department to review its legality.
However, other states are considering similar moves.
White House spokesman Bill Burton said Mr Obama "thought this was a good time to talk plainly with the American people about his views on immigration".
Immigration reform has been pushed down the president's agenda in recent months by issues such the Gulf of Mexico oil spill and overhauling the US health care system, correspondents say.