Ivanishvili may be anxious to fend off accusations that he intends to take Georgia back under Russian domination, and also to reassure the Americans that he is serious about deepening a relationship that was forged under his predecessor.
President Mikhail Saakashvili, whose party was defeated in Monday's parliamentary election, turned the former Soviet republic into a U.S. ally. The Kremlin, however, has refused to have any dealings with him since Georgia and Russia fought a brief war in 2008.
Diplomatic relations remain severed, which has complicated travel between the two neighboring countries and separated families. Georgia has a population of 4.5 million, and as many as 1 million Georgians live and work in Russia.
Particularly for Georgians old enough to have been educated in the Soviet Union, when Russian was taught in schools and they were all citizens of the same country, the rift has taken an emotional toll.
The economic consequences also have been painful for many Georgians. Trade between the two countries has been cut since Russia banned imports of Georgian wine, mineral water, vegetables and fruits in 2006 as tensions rose. Ivanishvili has promised to
But Saakashvili remains Georgia's president for another year, so no major changes are expected immediately.
"There is a hope that after Georgia's 2013 presidential election some warming up is possible in the trade and economic sphere, transport, and possibly humanitarian field," said Alexei Pushkov, who heads the foreign affairs committee in the Russian parliament.
Restoring diplomatic ties will be much more difficult because of a dispute over South Ossetia and Abhkazia, the two Georgian separatist provinces at the center of the 2008 war. Russia has recognized their independence and still has thousands of troops stationed on what most of the world still considers Georgian territory.
Russia has made clear it has no intention of changing its stance. "It's hard to expect a radical improvement in the political sphere because of the problem of Abkhazia and South Ossetia," Pushkov said.
The lack of diplomatic ties and Russia's tough visa requirements make it difficult for Georgians to travel to Russia unless they have immediate family living there.
Valentina Kevlishvili, a 60-year-old Russian married to a Georgian, wants to go to Russia to visit her father. She and her husband applied for visas at the consulate of Switzerland, which represents Russia's interest in Georgia.
"There they tell me that for me it's no problem, but my husband can't go because he's not a blood relative of my father," Kevlishvili said. "Those are the kinds of laws that Russia thinks up."
Georgia has abolished visas, so Russians can visit freely. Everyone arriving at the Tbilisi airport is welcomed at passport control with a small bottle of Georgian wine.
Natela Baguashvili, 47, who owns a small food shop in Tbilisi, remembers how strange it was for her and her Russian friends to find themselves on opposite sides during the war.
"I grew up with Russian friends and classmates, and we have stayed friends and we write back and forth," she said. "During the war they were worried about us. They love Georgia."
The Russian government has welcomed Ivanishvili's victory. Foreign Ministry spokesman Alexander Lukashevich said Wednesday that Moscow hopes Georgia will now be able to establish "constructive and respectful ties with its neighbors."
The head of the Russian parliamentary committee in charge of relations with former Soviet nations said there is hope for more positive relations. "Historically, geographically and culturally, our people are simply bound to have good-neighborly relations," said Leonid Slutsky.
Ivanishvili has strong business ties in Russia, and the Kremlin may be hoping to use him to bring Georgia back into the fold. Saakashvili has accused him of being a Kremlin stooge.
Ivanishvili denies this, and since his Georgian Dream coalition won the election, he has used every opportunity to reaffirm his commitment to making Georgia an integral part of Europe and a member of NATO.
NATO chief Anders Fogh Rasmussen reciprocated on Wednesday. "NATO is committed to our close relationship with Georgia and we look forward to making this relationship even stronger," Rasmussen said in a statement.
Ivanishvili took pains Wednesday to show his distance from Moscow.
"I have not received congratulations from Russia and have not contacted the Russian side," he said. "And moreover I am going to the U.S., to our main partner and friend."
Ivanishvili said he had an official invitation to visit Washington, but would wait to schedule a visit until after the U.S. presidential election in November.
He will become prime minister after the new parliament goes into session on Oct. 21.
Isachenkov reported from Moscow. Misha Dzhindzhikhashvili in Tbilisi, Georgia contributed reporting.