Russian President Vladimir Putin (R) shakes hands with US Secretary of State John Kerry during a meeting at the Kremlin in Moscow, Russia, on Dec. 15, 2015. Russian President Vladimir Putin on Tuesday met with visiting US Serectary of State John Kerry to discuss various issues, including the Syrian crisis.[Photo/Xinhua]

MOSCOW -- Russia and the United States pledged Tuesday joint efforts to push forward Syrian political process at the Friday peace talks held in New York.

After over-three-hour meetings in Moscow between Russian President Vladimir Putin and visiting U.S. Secretary of State John Kerry, Russia and the United States sesought some common ground on Syria's crisis and anti-terrorism fight.

"We support the idea of convening in New York another meeting of the International Syria Support Group at the ministerial levels this Friday," Russian Foreign Minister Sergei Lavrov said after earlier talks with Kerry at Kremlin.

It had previously been unclear whether the meeting would go ahead with Russia's participation.

Lavrov praised the meetings as concrete and substantive, adding the two countries are both determined to root out terrorist groups that pose common threat to the whole world.

"The talks in the morning and at night were concrete, focusing on progress in the Syrian settlement in the context of the fight against terrorism," Lavrov said at a joint press conference with Kerry after talks.

"We assume that everyone should contribute to the fight against terrorism and the promotion of Syrian political process, and Russia prefers to work in a collective format," Lavrov said.

Such an approach was reflected in previous Syrian peace talks in Vienna of Austria, and should include all key players that "influence one way or another on warring sides in Syria," according to Lavrov.

The minister also confirmed that the next meeting of the International Syrian Support Group (ISSG) would be held on Friday in New York, with efforts to draft a United Nations Security Council (UNSC) resolution on the basis of agreements reached during previous Vienna talks.

"We hope that through this follow-up, with the consent of all parties, we will be able to bring a draft UNSC resolution that confirms the principles laid down in the Vienna agreements reached on Oct. 30 and Nov. 14," Lavrov said.

The upcoming meeting would continue to work on the list of "generally recognized" terrorist organizations, as well as the formation of a Syrian opposition delegation, Lavrov said.

"They (oppositions) must be representative and must be ready to negotiate with Syrian government delegation in a constructive manner and in line with the principles approved by ISSG," Lavrov stressed.

On his part, Kerry urged to intensify efforts together with the UN on Syria's political settlement, adding that differences between Moscow and Washington were narrowed over classification of terrorist groups in Syria.

According to Kerry, the two sides also managed to find common ground on which Syrian opposition groups should take part in the negotiations aimed at resolving the four-year-old crisis, while it is unanimously agreed to exclude Daesh (Islamic State in Arabic) and al-Nusra Front from the negotiation process.

Although no details were given on the issue, Kerry stressed that what was agreed on bilateral basis should be informed on and discussed within ISSG.

Noting that the United States does not pursue a policy of isolating Russia, Kerry reaffirmed the ability of the two countries to work effectively while moving in the same direction and concentrating efforts in the fight against terrorism.

"The United States is ready to work with Russia to combat the Daesh," Kerry said, adding that coordination and data exchange is discussed during the meetings over anti-terror fight in Syria.

Nevertheless, Kerry still stressed the western sanctions imposed on Russia over the Ukraine conflict will be lifted as soon as the Minsk agreements are fully implemented.

Urging more action to fulfill Minsk accords and finally solve the crisis, Kerry said all parties to the conflict bear responsibility for the Minsk deal implementation.

Kerry's visit is the second in two years as U.S.-Russia relations has significantly deteriorated over the Ukrainian crisis.