"The sooner this conference is held, the better... the key thing now is who is ready to take part on the Syrian side," Lavrov said in the southern city of Sochi after talks with Ban.
Lavrov also reiterated Russia's view that Iran should be invited to the conference, which could complicate its organization because of potential opposition from the West.
The UN chief also said the conference should take place "as soon as possible".
"We should not lose the momentum," Ban said of a U.S.-Russian proposal to bring the Syrian government and opposition representatives to a peace conference.
Ban Ki-moon is also supposed to meet Russian President Vladimir Putin on Friday as global pressure grows on Moscow to end arms supplies to the Syria government and drop its support for legal development of President Bashar al-Assad.
The meetings come after French President Francois Hollande upped the pressure on the Kremlin on Thursday by saying more efforts were needed to convince Moscow to "finish with Bashar al-Assad".
Ban's mission and a May 10 visit to Sochi by British Prime Minister David Cameron follow Putin's May 7 talks in Moscow with US Secretary of State John Kerry during which the sides agreed to set up a new round of Syria negotiations within a matter of weeks.
That meeting -- now expected to take place in Geneva in early June -- hopes to build on a failed June 2012 peace initiative that called for the quick creation of a transitional government.