Nawaz Sharif appears on course to secure a majority in Pakistan's parliament and form the next government after claiming victory in Saturday's election.
Unofficial results suggest his Pakistan Muslim League has won easily, though he has reportedly opened talks with independents to guarantee a majority.
EU observers report that incidents of violence did not deter voters.
Mr Sharif was congratulated by Indian Prime Minister Manmohan Singh.
Mr Sharif was quoted as saying he would be happy if Mr Singh came to his inauguration, but it is unclear when a formal invitation will be issued.
The two spoke on Sunday, Mr Sharif told an Indian reporter.
"We had a long chat on the phone and then he extended an invitation to me and I extended an invitation to him."
The election appears to have paved the way for the first transition from one elected government to another in a country prone to military takeovers.
Mr Sharif is set to become prime minister for the third time.
Former cricketer Imran Khan, whose Movement for Justice Party (PTI) is in a close fight for second place, has promised to provide genuine opposition.
Analysts say Mr Sharif, 63, is in a far stronger position than the outgoing Pakistan People's Party (PPP) which led a weak coalition, often on the verge of collapse.
The PPP of late Prime Minister Benazir Bhutto was badly beaten in the election. It was one of several secular parties unable to campaign freely due to Taliban attacks.
Pakistani media say Mr Sharif's PML-N has so far captured at least 125 seats with the PTI and the PPP on around 30 each.
Analysts said the PML-N was likely to win around 130 seats and should be able to make up the required majority of 137 with support from independents and small parties.
Once it achieves a majority, Mr Sharif's party would be allocated most of 70 other parliamentary seats reserved for women and non-Muslim minorities.
An election commission spokesman said turnout had been around 60%. In 2008 it was 44%.
EU election observers said 64 people died on polling day itself, and that violence had distorted the electoral process in those areas affected.
But the mission added that at 90% of the 600 polling stations monitored, the conduct of the election was satisfactory or good.
On the whole, it said, there was a strong commitment by candidates and parties to the democratic process.
"The turnout in defiance of the threats against the process was an extraordinary vote of confidence in democracy itself," European Parliament member Richard Howitt told a news conference in Islamabad.
The Karachi stock exchange hit a record high on the expectation of a Sharif-led government. He is seen as favouring the free market and deregulation.
Ishaq Dar, a senator, has been chosen to serve as finance minister in the new administration. He held the same post in Mr Sharif's second government in 1998 and 1999 and again in 2008.
Mr Sharif - who was toppled in a military coup in 1999 and spent years in exile - held talks on Sunday on forming a government.
Imran Khan said the election would boost Pakistan's young democracy.
"We are now moving towards democracy. I congratulate the nation on the numbers in which they turned out to vote," he said.
But Mr Khan added that his party was collecting evidence of alleged vote-rigging.
Mr Khan has been bedridden after a fall at a campaign rally, but a doctor treating him told the BBC that the PTI leader would be walking again within two weeks, with the help of a temporary brace.
"He's virtually pain free, he's able to turn in bed independently," said Dr Aasim Yusuf, medical director of the Shaukat Khanum hospital in Lahore.
"He had no nerve or neurological damage in any case, so he's just recovering from his fractures. So we expect him to make a full recovery."
Dr Yusuf added Mr Khan was expected to progress quicker than normal because of his good health and fitness.
President Obama congratulated Pakistan on the election, welcoming the "historic, peaceful and transparent transfer of civilian power".
During his election campaign, Mr Sharif said he would end Pakistan's involvement in the US-led war on terror, without saying whether that included military operations against the Taliban and al-Qaeda.
On Monday, he said Pakistan had "good relations" with the US, and that any concerns on either side needed to be addressed.
The Indian prime minister said he hoped for a "new course" in relations between India and Pakistan.
Afghan President Hamid Karzai said he hoped for co-operation to root out what he called terrorist sanctuaries.
Both Pakistan and Afghanistan are engaged in a long battle with Taliban Islamist militants.
The triangular relationship between Pakistan, Afghanistan and the US will be tested more than ever as Nato withdraws combat forces from Afghanistan by the end of next year, says the BBC's Mike Wooldridge in Islamabad.
Mr Sharif said Pakistan would extend its "full support" over the withdrawal to "see that everything goes well and smoothly".
At home, Nawaz Sharif's government will have to tackle severe power shortages that damage the economy and hold back job creation, our correspondent reports.
It also faces domestic insecurity. On Sunday a suicide car bomber in the south-western city of Quetta attacked the residence of Mushtaq Shukhera, police chief of Balochistan province, killing at least five people and injuring 60.
Balochistan suffers from separatist violence and sectarian conflict between Sunni and Shia Muslims. No group has claimed responsibility for the attack.