The meeting comes amid rising tension between the two countries over Ukraine`s military campaign against pro-Russian separatists.
Ukraine said on Monday that its troops had captured 10 Russian servicemen in eastern Ukraine.
Russia has repeatedly denied supporting the rebels.
More than 2,000 people have died in months of fighting between Ukrainian forces and separatists in Donetsk and Luhansk regions.
The two regions declared independence from Kiev following Russia`s annexation of the southern Crimean peninsula from Ukraine in March.
Snap elections
Tuesday`s talks involving the two leaders - who last met in June - will come hours after Mr Poroshenko dissolved parliament and announced snap elections for 26 October.
In a televised address, he said many current MPs were backers of ousted President Viktor Yanukovych and that the majority of Ukrainians wanted a new parliament.
The summit in Minsk will also be attended by senior officials from the European Union which, along with the US, has imposed sanctions on Russia for failing to rein in the separatists.
Ahead of the talks, Russian Foreign Minister Sergei Lavrov said the West should not put all the onus on Moscow.
"I hope very much our Western colleagues... won`t just come with expectations we will somehow magically solve things for them. That will not work," he told a news conference.
Russia says Ukraine`s military campaign in the east is causing a humanitarian crisis.
Ukraine`s security service said its military had captured the 10 Russian paratroopers near the Ukrainian village of Dzerkalne, about 50km (30 miles) south-east of the rebel-held city of Donetsk.
"Russian soldiers have been detained with personal documents and weapons," a statement said, adding: "Investigators opened a criminal probe into illegal border crossing by armed Russian citizens."
Earlier on Monday, Ukraine`s military said a column of 10 tanks and two armoured personnel carriers had crossed from Russia and been heading towards the south-eastern port of Mariupol.
It said Ukrainian troops destroyed two tanks, blocking the area.
On Monday, heavy fighting was also reported in and around Donetsk.
In July, Ukraine`s governing coalition collapsed, requiring the president to call fresh elections if a new coalition could not be formed.
Mr Poroshenko said a new parliament was needed, partly to remove MPs who were blocking reform.
The BBC`s David Stern in Kiev says new elections do hold some risks for Mr Poroshenko.
If he is unable to end the fighting in eastern Ukraine before the October vote, he risks a voter backlash.
Anger is also rising among Ukrainians at the government`s inability to introduce reforms and tackle corruption, our correspondent adds.
Photo
More about:
