On the Pakistani front, however, things seem to deteriorate.

American and Pakistani officials expressed optimism last week that an agreement on re-establishing supply routes was imminent. Negotiators were narrowing their differences after three weeks of intense deliberations, they said, and it was hoped that an invitation for Pakistan to attend the summit would engender the good will needed to close the gap between the two sides.

The invitation was accepted, and Mr. Zardari arrived in Chicago on Saturday. But a deal on the supply lines remained elusive, and Mr. Obama would not meet with Mr. Zardari without it, American officials said.

The supply lines, through which about 40 percent of NATO’s nonlethal supplies had passed, were closed in late November after 24 Pakistani soldiers were killed in American airstrikes along the border between Afghanistan and Pakistan. The deaths capped a year of crises between the United States and Pakistan that put immense strain on the two countries’ already fragile relationship.

The failure to strike a deal on the supply routes ahead of the summit injects new tension into the relationship. “When NATO extended the invitation, we thought it would move the Pakistanis off the dime,” a senior American official said. Without the deal, “it’s going to be really uncomfortable” for Mr. Zardari at the summit, which runs through Monday, said the official, who requested anonymity to speak candidly about the talks.

American officials said the main sticking point was the amount NATO would pay for each truck carrying supplies from Karachi, on Pakistan’s Arabian Sea coast, to the Afghan border. Before the closing, the payment per truck was about $250. Pakistan is now asking for “upward of $5,000” for each truck, another American official said.

Mr. Obama called off a planned visit to Pakistan last year after the raid in Abbottabad, Pakistan, that killed Osama bin Laden. That Bin Laden had been living there confirmed what American officials had long suspected: Despite Pakistani protests to the contrary, the man behind the Sept. 11 attacks had been hiding in the country for years.

Mr. Obama did telephone Mr. Zardari a few hours after the raid to inform him that Navy Seals had done an incursion into Pakistani territory to kill Bin Laden, and during that conversation Mr. Zardari “spoke with emotion about the fact that these people were associated with the killing of his wife,” Benazir Bhutto, the senior official said.