The five-day ceasefire, which was agreed on October 17, ends at 10.00 pm local time (7.00 pm GMT), Efe news reported.
After receiving Erdogan at the Black Sea Sochi resort, Putin said "the situation in the region is very tense".
"We all understand it. I think that our meeting today, our consultations, are very necessary," Putin added in an encounter streamed on Russian public television.
Putin said he was confident the current level of Russian-Turkish relations would play a part in the settlement of all current issues affecting the region paving the way for answers to even the most complex of questions.
"There are many issues. The negotiations will be very complex, it is evident," Dmitri Peskov, Russian presidential spokesman, said shortly before the start of the bilateral meeting.
When asked about how long talks between Putin and Erdogan were expected to last, Peskov replied: "They will not be brief."
The Turkish government has vowed to resume its military offensive on the Turkey-Syria border the minutes the ceasefire expires if the Kurdish-led People's Protection Units (YPG) and Democratic Union Party (PYD) continue to have a presence in the area.
The Turkish government, which considers the Kurdish-led People's Protection Units (YPG) and Democratic Union Party (PYD) as terrorists, has vowed to resume its military offensive at 10:01 pm if one single Kurdish fighter was left in the region.
The YPG was a key US ally in the fight against the Islamic State terror organisation. The US announced the withdrawal of its troops on October 14 and Turkey announced its offensive into northern Syria shortly after.
The ceasefire was agreed between the Turkish PM and US Vice President Mike Pence on October 17.
Kurdish forces in the region said, however, that Turkish-backed Syrian militias had continued military action despite the agreement.
Erdogan is intent on ensuring his goal to force the withdrawal of all YPG members from a 32-kilometre-wide strip along the Turkish border is met, to pave the way for the creation of a so-called safe zone that, amongst other things, will allow the resettlement of some 2 million Syrian refugees.
Before leaving for Sochi, the Turkish President said, for now, Kurdish militias continued to leave the area occupied by Turkish troops in northeastern Syria.
Turkey's Defence Ministry added that an attack would be launched regardless of Russia's stance.
Moscow provides support for Syria's President Bashar Al Assad.
"Of course, a dialogue between Turkey and Syria is necessary, in which we are also willing to take on a conciliatory role, promoting such contacts," Russian Foreign Minister Sergey Lavrov said on Monday.
( With inputs from IANS )