Avigdor Lieberman took the rare step for an Israeli foreign minister Sunday of publicly criticizing Moscow, expressing "deep disappointment" over the previous day's meeting in Damascus between Russian Foreign Minister Sergei Lavrov and Hamas political bureau head Khaled Mashaal. Lieberman expressed "his deep disappointment" at the meeting, a brief statement put out by the Foreign Ministry said, adding that every meeting with Hamas pushes a diplomatic agreement further away and legitimizes terrorism. Lavrov said Sunday that Hamas was following a more "realistic" path after Operation Cast Lead. He urged the group to agree to a formal truce with Israel, noting that since the end of the war in mid-January there has been less rocket and mortar fire from Gaza into Israel. "We noticed a more realistic evaluation of the situation, the responsibility that Hamas feels not just for what happens in Gaza but for the fate of the entire Palestinian people," Lavrov said in remarks broadcast Sunday on Russia's state-run Vesti-24 television. Lavrov said he pressed Hamas to try to maintain a halt to rocket fire. "The ideal thing would be [to] conclude a formal truce," Russia's RIA-Novosti news agency quoted him as saying. He also took up Hamas's call for an end to a blockade of Gaza that Israel and Egypt imposed after the group seized control of the territory two years ago. He said he would discuss the blockade with Lieberman when the latter visits Moscow next month. Lavrov defended Russia's engagement with Hamas, saying that all sides must be included in peace efforts and that shunning Hamas helped lead to the Gaza crisis, according to RIA-Novosti. "This should have been done much earlier, when Hamas won elections in 2006 that everyone accepted as democratic, free and honest. But because of political prejudice, most Western countries did not recognize the Hamas government," he said. Unlike most other countries with whom Israel has close ties, Russia never stopped meeting Hamas, and consistently claims that in each meeting it presses the organization to accept the three conditions set by the Quartet for recognition - recognizing Israel, forswearing terrorism, and accepting previous Israel-Palestinian agreements. Russia is a member of the Quartet, together with the US, EU and UN. Mashaal has been in Moscow several times since his movement won the Palestinian Authority legislative elections in January 2006. Lavrov was in Damascus to attend a meeting of the foreign ministers of the Organization of Islamic Conference. Following his Saturday night meeting with Mashaal, Lavrov said he was convinced it was necessary to maintain contact with the organization. "We are certain that this is needed," the Interfax news agency quoted him as saying. Earlier this month, Lieberman launched a campaign to get Russia to cut off contacts with Hamas and Hizbullah, urging Italian Prime Minister Silvio Berlusconi to raise the issue with Russian leaders. Lieberman met with the Italian prime minister in Rome and asked him to convince the Kremlin that Hamas and Hizbullah were terrorist organizations working against Western interests in the Middle East. Meanwhile, in Damascus, Syrian President Bashar Assad told the Russian minister that Moscow's planned international Middle East peace conference would succeed only if it was well prepared. Moscow has for some two years expressed interest in a Middle East peace conference as a follow-up to the Annapolis conference. The official Syrian news agency SANA said Lavrov briefed Assad on Moscow's plan to "organize a conference on the Middle East in order to discuss the peace process." The Syrian president reportedly responded that "the conference must be well-prepared" and stressed the importance of setting out "objectives as well as the positions of those parties concerned" in the Israeli-Arab conflict. Assad also said it was important to know "the extent of Israel's commitment to achieve a just and comprehensive peace," SANA reported. AP contributed to this report.