"Many are caught in the crossfire", said UNICEF regional director Geert Cappelaere, according to AFP.
The group said the US -led coalition used white phosphorous in the night attacks on Raqqa.
On Thursday, a drone that USA officials say was likely connected to Iranian-supported Hezbollah forces fired on US -backed troops and was shot down by an American fighter jet in southern Syria near a base where the coalition is training Syrian rebels fighting the Islamic State group.
A group of journalists that visited the liberated neighbourhood of al-Mishlab on Friday were injured by mortar shells, when they visited the neighbourhood.
Qatar's FM: 'We are not ready to surrender'
These include cutting all links with Iran , the pan-Arab Muslim Brotherhood network and the Palestinian militant group Hamas. "No one has the right to intervene in our foreign policy", Sheikh Mohammed bin Abdulrahman Al-Thani said.
"Children are deprived of the most basic and life-saving necessities", he added, urging safe passage for those who want to leave the city.
Elsewhere on Thursday, US forces shot down a pro-regime drone in southern Syria after it fired at US-led coalition forces, said coalition spokesman Ryan Dillon. On Thursday, the US shot down an armed drone it said had attacked its units embedded with local opposition forces in the region.
They have also reportedly dug defencive trenches and tunnels to try to slow the SDF advance.
Pentagon spokesman Eric Pahon said "hundreds" of USA military personnel were taking part in the Raqa offensive.
But thousands have fled in recent months, and the United Nations humanitarian office estimates about 160,000 people remain in the city.
Doctors Without Borders (MSF) also warned that Raqa's civilians were left facing a "deadly choice".
Alleged Russia Hacking-Report Leaker Reality Winner to Plead Not Guilty
An FBI affidavit says victor confessed to copying and mailing the classified report when agents searched her home Saturday. President Trump has repeatedly decried leaks from inside his administration, arguing they endanger national security.
If civilians flee they also face the risk minefields and bullets from IS militants.
The Kurdish-Arab alliance known as the Syrian Democratic Forces (SDF) broke into Raqqa city's east earlier this week, months after they launched an operation to capture the extremist stronghold.
The sources have published video footage and photographs of the bombs exploding over the city that is under attack on three sides by Kurdish forces supported by the US-led worldwide anti-ISIS coalition.
US defense officials said the weapon fired by the drone did not detonate and no one was hurt.
Chance of showers, thunderstorms to persist as week progresses
A high pressure begins to move in on Friday that makes us mostly sunny and temperatures are in the mid-70s. MONDAY NIGHT: Partly cloudy skies with mild and muggy conditions develop with a low of 69 degrees.