According to the Duma head, bilateral relations have been developing intensively lately.
The work of the bilateral commission for economic, scientific and technical cooperation bears witness to the intensified development of cooperation, he said, pointing out Croatia's decision to join in the South Stream project for a gas pipeline transporting Russian natural gas to the Black Sea and further to Europe.
"We were glad to hear that Croatia has joined South Stream," he said.
The Croatian official, who was on an official visit to Russia, said at the meeting with Gryzlov that both countries were interested in the enhancement of their cooperation in all fields.
This visit is taking place in Russia at a time of enhancement of bilateral relations following Croatian Prime Minister Jadranka Kosor's two visits to Russia earlier this year, Bebic said.
He went on to say that the two countries were working on new projects.
It was confirmed that Croatia is in the South Stream project and new ecological studies on a planned implementation of the Druzba Adria project "will open up new possibilities", he said.
Bebic and his host were agreed that bilateral parliamentary cooperation was developing very well.
Gryzlov said that the Russian-Croatian friendship group in the Duma "is ardently working on the development of relations".
When it comes to culture, Days of Russia are being held in Croatia this year, and next year Days of Croatia will be held in Russia, he said, adding that tradition also linked the two countries.
He spoke about cooperation in tourism, adding that this year 130,000 Russian guests have been in Croatia.
Trade between the two countries, which reached nearly two billion US dollars in 2008, saw a significant fall in 2009 due to the global economic crisis, but it is now slowly recovering, Gryzlov said.
On Monday, Bebic also held talks with some other officials in the Russian parliament and on Tuesday he will visit the Russian foreign ministry and travel to Saint Petersburg.