Mr. Assad met with Mr. Putin in the Black Sea resort of Sochi.
Putin spokesman Dmitry Peskov said Assad informed the Russian leader of his decision to "send a delegation to the U.N." to discuss overhauling the country's constitution.
Russian Federation is a key ally of Assad and has provided support which has allowed the Syrian regime to make territorial gains in recent months against rebels.
At the meeting, which had not been announced in advance, Putin congratulated the Syrian leader on what he said were significant successes on the battlefield achieved by the Syrian military.
Russia, Iran and Turkey have been attempting to resolve the conflict in the talks that started previous year in Astana in competition with a USA and UN-backed Geneva initiative.More news: Ambassador Danon responds to Kuwait's United Nations draft resolution on Gaza
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According to the Kremlin statement, Assad said "stability is improving" in Syria, "opening the door to the political process we started some time ago".
The informal summit between the two leaders, which, has a broad-based agenda on global and regional issues, is expected to see the discussions on global terrorism, situation in Afghanistan-Pakistan, Syria, Islamic State (IS), the sources added.
Western sanctions have complicated sales of Russian arms, but Moscow is ready to work under the challenging conditions and export more military equipment to other countries than planned, Tass news agency quoted Vladimir Kozhin, a presidential aide, as saying in March.
The Britain-based Syrian Observatory for Human Rights said the last of seven batches of displaced left the area Wednesday in a convoy, bringing the total evacuated to 34,500 people, including fighters and civilians, who have departed to other rebel-held areas in northern Syria.
Putin and Assad met on the eve of a meeting in Sochi between Putin and German Chancellor Angela Merkel, the first face-to-face talk of the year between the veteran leaders.