The UN refugee agency has reiterated its appeal to all parties to ensure safe passage for convoys delivering humanitarian aid to civilians inside Syria.
The death toll continues to increase, the latest casualties reported Thursday by Syrian government media which said rebel mortar fire has hit the University of Damascus, killing 15 students after the faculty of architecture was hit.
The United Nations says at least 70,000 people have been killed in the fighting in Syria since the uprising against President Bashar al-Assad began two years ago.
The office of the UN High Commissioner for Refugees said this week the number of people internally displaced in the ravaged country is rising toward 4 million.
"According to the UN's latest estimates, at least 3.6 million people are internally displaced in Syria," UNHCR spokesman Adrian Edwards told journalists.
In the current security environment, several convoys have had to be cancelled or delayed the UNHCR said.
The Syrian Arab Red Crescent has faced difficulties accessing the vulnerable in the country's north where rebels have bases.
This is depriving many Syrians of vitally needed help.
"UNHCR is working with government and non-government parties to see that aid gets through, however right now assistance is only reaching a fraction of those in need," said Edwards
Despite the security difficulties, UNHCR has been working to scale up its operations.
"Currently, our goal is to deliver relief items to at least 1 million people by June 2013, and we hope to reach many more people in the months after that.
"As of 20 March, we had delivered relief items to over 437,000 people in some of the most affected provinces, including Aleppo, Al Hassakeh, Ar-Raqqah, Damascus, Daraa, Deir Ezzor, Hama and Idlib," said Edwards.
Some of the church-backed agencies working in Syria are the Lutheran World Federation, a member of the ACT Alliance.
LWF member churches contributing to the Syrian refugees' appeal issued under ACT Alliance also include the Evangelical Lutheran Church in America, Church of Sweden, and Evangelical Lutheran Church in Bavaria (Germany).
Support also came from the German Protestant aid agency Diakonie Katastrophenhilfe, DanChurchAid and the United Church of Canada.
Those agencies said they received government funding from Denmark's international development agency DANIDA and the German and Czech Ministries for Foreign Affairs.
Aid includes bedding, shelter, household items and clothes. The items were delivered directly by UNHCR or by local NGOs and the Syrian Arab Red Crescent.
"We received the shelters during the rains, but before the snowfall. Our first night in the prefabricated shelter was the first night we felt safe and warm in Za'atri refugee camp," Omm Yaser told the LWF.
Yaser's family is among the 158,000 Syrians who were living at the Za'atri refugee camp in northern Jordan by mid-March.
After two years of intensifying conflict at home, more than 1.2 million Syrian refugees are registered or awaiting registration in Jordan, Lebanon, Iraq, Turkey and Egypt, with new arrivals estimated at around 8,000 a day, according to the UNHCR.