ST. PETERSBURG, Russia — After two days of intense lobbying, President Obama left a summit with world leaders Friday with some expressions of support for a strong U.S. response to Syria’s alleged use of chemical weapons, but well short of an international coalition that might help persuade reluctant lawmakers.

The president had hoped to use the meeting of the Group of 20 nations to build pressure on Congress as it considers whether to authorize missile strikes against Syrian President Bashar Assad’s government.

Before leaving for Washington, Obama said at a news conference that he will make his case in an address from the White House on Tuesday, an acknowledgment that his plans remain divisive abroad and at home.

“This is not something that I think a lot of folks around the world, you know, find an appetizing set of choices,” he said. “But the question is, do these norms mean something? And if we’re not acting, what does that say?”

The president had to settle for a carefully worded statement backed by representatives of 10 countries that said Assad should be held accountable for an alleged nerve gas attack on the Damascus suburbs two weeks ago, but did not explicitly support military action or promise participation. Among the leaders who did not endorse the statement was the summit’s host, Russian President Vladimir Putin, who is Assad’s closest ally.

Obama and Putin pulled up two chairs in a corner and talked for more than 20 minutes Friday, almost entirely about Syria. The leaders have exchanged harsh words, but Putin called the talk “friendly” and Obama said it was “candid and constructive.” But it did not break their impasse over how to respond to the suspected chemical weapons attack or how to end the 21/2-year-old Syrian civil war.

“We both remained unconvinced by each other’s opinion,” Putin said at a news conference. “But there is a dialogue. We hear each other, we understand arguments, but we don’t agree with them.”

Putin added that Russia will continue to supply weapons to Assad in his battle against the rebel opposition. Local news reports said three Russian ships and possibly a fourth were headed to the eastern Mediterranean, where the United States has four guided missile destroyers and an amphibious ship with 300 Marines.

At a dinner that stretched into the morning hours Friday, world leaders vigorously debated Obama’s plan, with many saying the president should wait for the United Nations to complete a report on the Aug. 21 attack and sanction a response. Obama argued that the U.N. Security Council was paralyzed by disagreement. Russia and China, which have veto power, have blocked efforts at the Security Council to put pressure on Assad.

Obama’s plan for what he stresses will be “limited and not open-ended” strikes also remains unpopular in the United States. The statement and the heated discussion were reminders of what Obama has called “a heavy lift” as he seeks to sell lawmakers and the American public on the need for a military response.

Jon B. Alterman, director of the Middle East Program at the Center for Strategic and International Studies, said the problem for Obama isn’t whether he has international support but American support. “The people who matter right now are Americans,” Alterman said. “If he can’t convince them, it’s catastrophic for his presidency.”

The Senate could take the first vote on the issue as soon as Wednesday, but the House should “expect a robust debate” and a vote in the “next two weeks,” said Majority Leader Eric Cantor, R-Va.

Although the Senate Foreign Relations Committee quickly approved a resolution this week, the already challenging politics have since become more complicated. Sen. Joe Manchin III, D-W.Va., who opposes the resolution, was consulting his colleagues on a proposal for a nonmilitary response.

In the House, Rep. Chris Van Hollen, D-Md., said the Senate resolution, which aims to shift the momentum in the civil war toward the opposition, “opens up a Pandora’s box.”

“I think the administration runs an incredible risk, if they try to placate those who want to expand American military intervention in Syria, because they risk losing support of the overwhelming majority of members,” he said after meeting with Vice President Joe Biden.

The Obama administration had resisted intervention in the war, but switched course after the alleged chemical weapons attack, which U.S. intelligence agencies have concluded killed more than 1,400 people.

On Friday, Obama compared his bid for action to humanitarian intervention in Kosovo in 1999 and the U.S. failure to stop the genocide in Rwanda in 1994. He cast the international division as the result of war-weary leaders “rationalizing not making tough choices.”

The United States alone, he said, shoulders the burden of enforcing international agreements on human rights and chemical warfare.

“There are times where we have to make hard choices if we’re going to stand up for the things that we care about. And I believe that this is one of those times,” Obama said.

But Obama did not persuade a single ally to endorse a specific action. Immediately after he spoke, the White House released the joint statement from Australia, Britain, Canada, France, Italy, Japan, South Korea, Saudi Arabia, Spain and Turkey, as well as the United States.

The statement did not specifically endorse military action, but concluded: “We support efforts undertaken by the United States and other countries to reinforce the prohibition on the use of chemical weapons.”