"Silence against Gaza catastrophe is not wise and people of Gaza will not tolerate repetition of former tyrannical conditions and continuation of several years of siege," Rouhani said during the telephone conversation on Tuesday.
He noted that regional conditions necessitate closer cooperation and consultation between Iran and Qatar.
The Iranian president said that all Muslims are in a big historical test, adding, "Unity and cooperation is needed among Muslims to change living condition of the people of Gaza and attain sustainable ceasefire.
The Qatari emir, for his part, underlined the need for cooperation among Muslim states to break the siege of Gaza, and said, "Palestinian resistance movement defends it own pride and no one can prohibit it from it."
He also welcomed the meeting of the Palestinian Committee of the Non-Aligned Movement (NAM) due to be held at the ministerial level in Tehran later this week.
The foreign ministers of the Non-Aligned Movement are slated to take part in an emergency meeting of the block's Palestine Committee in Tehran to discuss the aggravating conditions in the Gaza Strip, Iranian Foreign Ministry Spokeswoman Marziyeh Afkham announced on Sunday.
"The one-day meeting of NAM's Palestine Committee will be hosted by Iranian Foreign Minister (Mohammad Javad Zarif) in Tehran," Afkham said.
She noted that the ambassadors of the member-states of NAM's Palestine Committee, in a meeting held in New York earlier this month at Iran's initiative and presided by Iran's Ambassador to the UN Hossein Dehqani, selected Tehran for hosting the day-long emergency meeting.
"Subsequent to the outbreak of the recent crisis in Gaza and the order of President Hassan Rouhani and within the framework of the intensive diplomatic efforts made by Iran as rotating head of the NAM, several emergency and intensive meetings have been held in New York in the past 10 days as a result of the prompt action of the Iranian mission at the UN following a relevant order by Dr. Zarif to the mission," Afkham said.
"Ways of utilizing the political capacities of the NAM member-states and relevant attempts and actions have been discussed and the (emergency) meeting of the NAM's Palestine Committee will be held within the same framework," she added.
Earlier this month, President Rouhani, as the Head of the NAM, in a declaration seriously condemned the recent massive attacks by the Israeli forces against the innocent people of Gaza Strip, and called on international bodies and world states to force Tel Aviv to stop its blind raids on civilians.
"Siege of Gaza Strip must be fully and immediately lifted and humanitarian aids must be forwarded to the Palestinians in need of them there," said President Rouhani in the NAM declaration.
"The intensive air strikes against the residential areas of Gaza that have killed dozens of Palestinians so far and wounded so many others, including many women and children, once again echoed the sad tragedy of the Palestinian nation, and the obvious breaching of the entire international law by the Zionists before the open eyes of the world nations" the NAM declaration said.
"The recent aggressive acts have led to the creation of a catastrophic condition that has put at stake both the regional and the international peace and security," it added.
"Military invasion against Gaza Strip takes place under such conditions that the region is still due to the lingering siege of Gaza throughout the past many years suffering from a dilemma due to the heavy shortage of medical and health facilities and the Palestinians face numerous hardships even for curing their wounded victims of the recent attacks," the declaration went on to say.
"The occurrence of a great human catastrophe is feared under the current conditions and while expressing deep concern about its occurrence in Gaza Strip, I emphasize the need for offering humanitarian aids to the people of that region, immediately," the Iranian President underlined.
"I, as the president of the Islamic Republic of Iran, and the rotating head of NAM, seriously condemn the systematic, illegal, and inhumane crimes against the Palestinians, and call on the entire concerned regional and international bodies to heed their legal responsibilities immediately, in line with full lifting of the Gaza siege and in forwarding of humanitarian aids for the Palestinian people, as well as blocking the path for more aggressive acts and the greater massacre of the oppressed Palestinian people through adoption of an effective legal and international mechanism to pursue and put to trail the criminal Zionists," President Rouhani stressed.
The NAM declaration ended with deep pessimism on the impotence of the UN Security Council for adopting immediate measures to stop the ongoing aggressions and asked the UNSC members to immediately heed their responsibilities for putting an end to those unjust aggressions.
Israel has been pounding the blockaded Gaza for 23 consecutive days, killing at least 1,260 people and injuring more than 7,000 others.