They also discussed a project for constructing a pipeline connecting Finland to Russia's huge oil reserves.
The talks were the main point of Finnish Prime Minister Paavo Lipponen's first official visit to Moscow this week.
Lipponen's Russian counterpart, Viktor Chernomyrdin, hailed the talks as "dynamic and productive," and went on to praise the "huge potential" for cooperation between the two countries.
"We must do everything to fulfill this potential," Chernomyrdin said. "We must not stand still."
But economic tensions -- especially over trade and debt issues -- have been running high, and they dominated Monday's talks.
The Finnish delegation expressed concern over a proposed sharp jump in Russian transport tariffs, which could threaten the delivery of Russian timber to Finland, Interfax reported.
"These tariffs are our biggest bottlenecks on trade," Ole Norrback, Finland's Minister of Trade and Industry, said Monday. "First, we must remove these bottlenecks, and then the possibilities for cooperation will be wide open."
Finland, one of Russia's leading trade partners, had also been worried about a hike in import tariffs on food and other goods, introduced by the Russian government July 1.
Russian Deputy Prime Minister Oleg Davydov said Russia had agreed at Monday's meetings to lower some duties on imports from Finland in exchange for technical and humanitarian assistance, Interfax said.
Both sides debated alternative ways for Russia to repay its debt to Finland, which is about $1 billion.
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