"We received with satisfaction this news [about the agreement], which confirms further progress on the way to national reconciliation," Mikhail Kamynin said in a statement.
A Hamas official earlier announced that his organization and Fatah, led by Palestinian President Mahmoud Abbas, reached an agreement on a political platform of the new Cabinet.
According to the agreement, Hamas and Fatah will be able to delegate a set number of ministers, who are not professional politicians, to form a new government, while Islamist Hamas, which controls the current Cabinet, will have the right to nominate a new prime minister.
The Mideast Quartet, which includes Russia, the United States, the European Union and the United Nations, has recently increased its pressure on Hamas to have it recognize Israel's right to exist, abandon violence, and respect existing peace pacts after the militant Islamist grouping, blacklisted by many Western governments as a terrorist organization, won a landslide victory in legislative polls in January.
The Palestinian Authority has since then been facing an international aid boycott, which the mediators say will not be lifted until the Hamas-led government meets all the demands.
Russia's Deputy Foreign Minister Alexander Saltanov said in September that Hamas should demonstrate its readiness to cooperate with the conditions and demands set out by the Quartet.
