U.S. Sen. Richard Lugar, R-Ind., met over the weekend with Georgian opposition leaders, some of whom claim the government is harassing their supporters.

Lugar, the ranking Republican member of the Senate Foreign Relations Committee, met Sunday with representatives of the "Georgian Dream" coalition, including David Usupashvili, leader of the Georgian Republican Party, and Our Georgia-Free Democrats leader Irakli Alasania, Trend news agency reported.

Giorgi Targamadze, leader of the Christian Democratic Movement, and former Georgian Foreign Minister Tedo Japaridze -- currently political adviser to opposition presidential hopeful Bidzina Ivanishvili -- were also in attendance, the news agency said.

The meeting came in the run-up to the Oct. 1 parliamentary elections, seen in the West as test of Georgia's democratic progress under Saakashvili.

The Georgian Dream coalition has emerged as a credible challenger to the president's United National Movement Party, which has been in power since the 2003 Rose Revolution that ousted the nation's pro-Kremlin leadership.

Georgian Dream supporters say they are being targeted for harassment by the government's supporters, while Saakashvili claims Georgia under his presidency has become a beacon of democracy and that his opponents are being controlled by Russia.

The European Union has voiced concern about tensions building in the country preceding the election, in which several violent skirmishes have broken out and journalists have been arrested.

Lugar, who was completing a weeklong trip to Georgia, Russia and Ukraine, didn't comment after the Tbilisi meeting but some of the opposition leaders did.

They said the senator, while reiterating U.S. support for the country, also talked with them about the upcoming election and the "environment" in which it was being held, Georgian broadcaster Rustavi 2 reported.

Targamadze said Lugar stressed it was important to "finish (the) domination of one party over the Parliament and the whole political space."

"All of us, who know the Georgian politics, understand this very well -- our American supporters who back up Georgia democratic future, support united Georgia for all generations, also understand this well," he said.

Alasania of the Our Georgia-Free Democrats party said the need for fair and impartial vote-counting was discussed in the Lugar meeting.

"We all understand that in the process of the vote-counting, no violations must take place and the Georgian people's decision must be correctly depicted by the election commission," he said.

Also discussed, Alasania said, was the United States' support for Georgia's "territorial integrity and withdrawal of the Russian troops from the territory of our country" -- a reference to the breakaway Georgian regions of Abkhazia and South Ossetia.

Lugar also met with Saakashvili in Georgia, appearing with the president on a tour of a $100 million, U.S.-funded biological research facility near Tbilisi, Civil Georgia reported.

The Central Public Health Reference Laboratory, opened in 2011, Sunday was named after Lugar to honor his "efforts to safeguard the world from stockpiles of nuclear, chemical, and biological weapons," the U.S. Embassy said.

"The Soviet Union, Russia has never made such investments in Georgia," Saakashvili said during the event.