The White House has strongly condemned a visit to Moscow by Syrian President Bashar al-Assad.
A spokesman criticised Russia for putting on a "red carpet welcome".
The Syrian leader's trip on Tuesday came three weeks after Russia began air strikes in Syria against Islamic State militants and other forces.
It was Mr Assad's first overseas trip since civil war broke out in Syria in 2011. The conflict has claimed more than a quarter of a million lives.
On Thursday, a team of Russian MPs is due to meet President Assad and the head of the Syrian parliament in Damascus.
While in Moscow, Mr Assad made a point of expressing his gratitude for Russia's military intervention in the conflict.
He said Russia's involvement had stopped "terrorism" becoming "more widespread and harmful" in Syria.
For his part, Mr Putin said Moscow's hope was that a "long-term resolution can be achieved on the basis of a political process with the participation of all political forces, ethnic and religious groups".
The BBC's Steve Rosenberg in Moscow says that by hosting the Syrian leader, President Putin was sending a clear message to the West - that Moscow is a key player in the Middle East, and that there can be no solution to the Syrian conflict without Russia's involvement.
"We view the red carpet welcome for Assad, who has used chemical weapons against his own people, at odds with the stated goal by the Russians for a political transition in Syria," White House spokesman Eric Schultz told reporters.
A state department official said it was not surprised by the visit, but the main US concern was Russia's continued military support, which he said had emboldened the Assad government - something that would only serve to lengthen the civil war.
In the wake of Mr Assad's surprise visit, President Putin spoke to a number of Middle Eastern leaders to brief them.
They included the leaders of Saudi Arabia and Turkey, which give support to Syrian rebels.
Mr Putin also spoke to the Egyptian and Jordanian leaders, Russian news agencies said.
Turkish Prime Minister Ahmet Davutoglu said that after the visit "the Syrian government has no legitimacy left".
Analysis: Diplomatic correspondent Jonathan Marcus
President Assad's surprise visit to Moscow represents a sign of growing confidence for the embattled Syrian president.
Firstly he feels it safe to leave Damascus for the first time since the civil war in Syria erupted. It is also a visible symbol of Russia's confidence in the current Syrian regime.
The visit leaves little doubt that for now at least President Putin is intent on shoring up Mr Assad's position.
But the trip may also mark a new stage in Russia's efforts to roll out a diplomatic plan alongside its military intervention in Syria. Mr Putin has been speaking to other regional players: the Turks, the Saudis, the Jordanians and the Egyptians.
There's a simple message here. The road to any diplomatic settlement now runs through Moscow and, for now at least, Mr Assad has to be part of any interim solution.
Russia launched air strikes in Syria on 30 September, saying they were hitting IS positions - which are also being targeted by US-led strikes.
Western countries and Syrian activists say Russian planes have been focused on hitting non-IS targets in order to shore up the position of the Syrian army, a claim Moscow denies.
Why is there a war in Syria?
Anti-government protests developed into a civil war that, four years on, has ground to a stalemate, with the Assad government, Islamic State, an array of Syrian rebels and Kurdish fighters all holding territory.
Who is fighting whom?
Government forces concentrated in Damascus and the centre and west of Syria are fighting the jihadists of Islamic State and Jabhat al-Nusra, as well as less numerous so-called "moderate" rebel groups, who are strongest in the north and east. These groups are also battling each other.
What's the human cost?
More than 250,000 Syrians have been killed and a million injured. Some 11 million others have been forced from their homes, of whom four million have fled abroad - including growing numbers who are making the dangerous journey to Europe.
How has the world reacted?
Iran, Russia and Lebanon's Hezbollah movement are propping up the Alawite-led Assad government, while Turkey, Saudi Arabia and Qatar back the more moderate Sunni-dominated opposition, along with the US, UK and France. Hezbollah and Iran are believed to have troops and officers on the ground, while a Western-led coalition and Russia are carrying out air strikes.