The two met Tuesday night, Israel Radio reported, after weeks of turmoil and protests in the former Soviet state that saw the president overthrown and a warrant issued for his arrest.
Tuchynov, the former parliament speaker, told Bliech that the new leadership is doing everything it can to end the anarchy of recent months, the radio said.
Ukraine's parliament voted Tuesday to send fugitive President Viktor Yanukovich to the International Criminal Court, while expressed concern about "signs of separatism" in Russian-speaking Crimea.
A resolution, overwhelmingly supported by parliament, linked Yanukovich, who was ousted by the legislature on Saturday and is now on the run, to police violence against protesters which it said had led to the deaths of more than 100 citizens of Ukraine and other states.
Meanwhile, Jewish Agency chief Natan Saransky said last week that the organization that would extend immediate emergency assistance to the Jewish community in Ukraine, and help secure Jewish institutions in the country.
"The Jewish community of Ukraine, which counts some 200,000 members, is one of most vibrant Jewish communities in the world, with dozens of active Jewish organizations and institutions," said Sharansky.
"Recent events have shown that we must strengthen these institutions' security measures. We have a moral responsibility to ensure the safety and security of Ukraine's Jews."
There has apparently been a rise in anti-Semitic attacks in Ukraine, with members of the Jewish community being beaten and assaulted in the street.
Last month, 30-year-old Dov Ber Glickman, 30, a member of Kiev's Jewish community, was assaulted by three youngsters as he was making his way home from a Shabbat meal in the capital's Podil neighborhood.
A week earlier, an Israeli-born teacher was beaten up at the entrance to his building. Locals said the attack was in the same area and carried out in the same style as the assault on Glickman.