Assad, who has also been assisted by Iran during the conflict, has made few trips abroad since the war began in 2011.
Putin told him the main problem in Syria was the presence of foreign forces without permission or a U.N. mandate, "which clearly runs counter to international law", the Kremlin said on Tuesday.
This "undermines your ability to use your best efforts to consolidate the country and promote recovery at a pace that would have been possible if the legitimate government controlled the entire country".
The Syrian state views the U.S. and Turkish forces as occupiers, while Russian forces and Iranian-backed militias are there at the government's invitation.
"Terrorists sustained very serious damage, and the Syrian government, headed by you, controls 90% of the territories," Putin said, according to the Kremlin.
However, according to other assessments, he holds less than this. Issuing its latest report on Syria on Tuesday, the U.N. Commission of Inquiry put the portion under Assad's control at just 70%.
Its latest report documented increased violence, fighting and rights violations in the year to the end of June, including arbitrary detention by government forces. It said Syria was unsafe for refugees to return to.
The meeting with Assad on Monday was Putin's last public engagement before he announced on Tuesday that he was self-isolating as a precaution after several members of his entourage fell ill with COVID-19.
Assad and his wife both recovered from COVID-19 earlier this year.
The Kremlin said Assad had thanked Putin for providing humanitarian aid and for his efforts to halt the "spread of terrorism".
He lauded what he called the success of Russian and Syrian armies in "liberating occupied territories".
Assad also said the sanctions imposed by some nations on Syria were "anti-human" and illegitimate.
The United States tightened sanctions against Syria last year, saying it wanted to force Assad to stop the war and agree to a political solution.
The Syrian state news agency SANA said the two leaders had discussed cooperation between their armies in "combating terrorism and completing the liberation of the land that is still under the control of terrorist organisations".
(Reporting by Vladimir Soldatkin and Andrew Osborn; Writing by Vladimir Soldatkin and Tom Perry; Editing by Clarence Fernandez, Robert Birsel and Kevin Liffey) ((firstname.lastname@example.org; +7 495 775 12 42;))