"The images we see on television today are not very encouraging in terms of lawlessness in certain parts of the country," Kathleen Hunt of Care International said Wednesday.
She said humanitarian aid won't get through unless there is order.
"We need respect for international humanitarian law, we need the independence to move around and do our assessments and we need security," she said.
UNICEF is still in Iraq, but UNICEF USA president Charles Lyons says it can do more with law and order.
"Security is the essential precondition to effective humanitarian work," he told CBS News Early Show co-anchor René Syler.
UNICEF's staff members still in Baghdad are nationals; they live in Iraq and know their communities, "and they will make judgments every single day as to whether they can get something done or not," said Lyons. "Their first responsibility is to themselves and their families to be safe."
Until order is restored, UNICEF's aid will be spotty, he said.
"You can't operate in an environment where there is shooting."
In a speech broadcast Thursday to the Iraqi people from planes flying over the country, President Bush promised there would be aid.
"We are taking unprecedented measures to spare the lives of innocent Iraqi citizens, and are beginning to deliver food, water and medicine to those in need," he said.
Many aid representatives insisted that the role of coalition troops in humanitarian and reconstruction efforts should be limited.
Representatives of several non-governmental organizations, including Save the Children and Amnesty International, expressed their concerns at a forum Wednesday with members of the U.N. Security Council.
U.S. Ambassador John Negroponte told reporters that security in Iraq will improve as the remnants of Saddam Hussein's regime are stamped out.
"As coalition presence increases in that country and as the level of resistance from Iraqi forces declines, the security situation should improve and it should be easier for these agencies to operate in various parts of Iraq," he said.
Pakistan's U.N. ambassador, Munir Akram, said food supplies for many families in Iraq would last two or three weeks at most, and that electrical problems were threatening water purification systems.
"There will be tremendous tolls taken on malnourished kids who are now drinking foul water if, in fact, the security situation doesn't improve so that the humanitarian workers" can do their jobs, said Lyons.
The United Nations says about $720 million in relief supplies are on trucks and ships bound for Iraq, but it still needs $2.2 billion in emergency funds.
A Los Angeles-based humanitarian agency loaded up five tons of medical supplies Wednesday that will be shipped to the Persian Gulf to help rebuild Iraq's health infrastructure.
Operation USA is sending $300,000 dollars worth of sutures, surgical gowns, multivitamins and other medical supplies.
The shipment is expected to arrive in the Persian Gulf within a month.
In an effort to speed aid to Iraq, the Security Council authorized U.N. Secretary-General Kofi Annan to review nearly $16 billion in contracts approved under the oil-for-food program and give priority to those that could be used immediately for humanitarian relief.
The U.N. program, established after the 1991 Gulf War, uses Iraq's oil revenues primarily to pay for food and medical supplies.
"We believe the U.N. has a vital role to play, and that was a very carefully chosen word. It means the U.N. is very important to the process," Secretary of State Colin Powell told the Los Angeles Times. "We need an endorsement of the authority and an endorsement of what we're doing in order to begin selling oil in due course, and in order to make sure that humanitarian supplies continue to flow in for the Oil for Food program."