Ivanov's statement came hours after the gunmen surrendered at the end of a 12-hour standoff in Istanbul.
The gunmen had issued a statement saying the action was aimed at protesting Russian attacks in the Caucasus, where Chechen rebels and Russian forces have been fighting since September 1999.
Istanbul Police Chief Kazim Abanoz said 120 people were held hostage. The Russian Foreign Minister's spokesman Alexander Yakovenko said there had been four Russians among the hostages.
The US Embassy said 40 Americans had been staying at the hotel, but it was not clear if they were among the hostages.
The hostage taking is likely to have a devastating impact on Turkey's tourism industry, just as the country is struggling to recover from an economic crisis.
Interior Minister Sadettin Tantan said Turkey could not condone the hostage-taking, "especially at the start of the tourist season."
Unless security for Russians in Turkey is ensured, "contacts between our countries may suffer seriously," Ivanov said. "You know that every year, not a few Russians visit Turkey, including for vacations."
The Turkish government hopes rising tourist numbers will help bring much-needed foreign currency into the battered economy. Some 10 million tourists visited Turkey last year.
Speaking after a meeting with News Zealand Foreign Minister Phil Goff, Ivanov said Russia has repeatedly urged Turkey to put an end to the activities of "terrorist organizations" on its territory, the news agency ITAR-Tass said.
"Unfortunately they still feel free on Turkish soil", he was quoted as saying, adding that one of the gunmen had participated in an attack on a Russian ferry in Istanbul in 1996.
Turkish Prime Minister Bulent Ecevit meanwhile assured that Turkey would not permit those supporting Chechen rebels to take refuge in Turkey.
"Necessary measures will be taken in this regard," Ecevit said.
Last month, Chechen hijackers seized a Russian airliner after it took off from Istanbul. The plane was stormed by special forces in Medina, Sauid Arabia, after the hijackers threatened to blow up the aircraft. A crew members, a passenger and one of the hijackers were killed.
No one was injured in the 12-hour standoff, police said. Thirteen gunmen were taken into custody.
The gunmen agreed to surrender after Tantan visited the hotel and held indirect talks with them, said Mehdi Nusret Cetinbas, head of the Istanbul-based Caucasus Association, who added that he had acted as an intermediary in the negotiations.
The interior minister, who is in charge of Turkey's internal security, said he had not bargained with the gunmen but persuaded them to give themselves up, saying they were causing "more harm than good," private CNN-Turk elevision reported.
The gunmen, armed with automatic rifles and shotguns, stormed the Swissotel late Sunday night. They issued a statement saying their action was aimed at protesting Russia's "bloody attacks" on separatists in the Caucasus, where the Russian republic of Chechnya is located.
Turks strongly sympathize with their fellow Muslims in Chechnya. Some 80 Caucasus organizations operate in Turkey and many have been active in promoting the Chechen cause.
Chechen rebels drove Russian troops out of Chechnya in a 1994-96 war. Russian forces returned to the breakaway republic in September 1999, and fighting has continued.
The struggle of Chechen rebels against Russia is popular in Turkey. Turks not only share the Islamic faith with Chechens, but some 5 million Turks trace their roots to Caucasus areas such as Chechnya. About 25,000 Chechens live in Istanbul and western Turkey.
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