An international agreement on a third emblem for the international Red Cross has been delayed by a dispute between Syria and Israel.
Israel could use the new symbol to operate as an ICRC member
Syria has insisted on an accord giving its humanitarian workers access to the Israeli-occupied Golan Heights.
A 192-nation conference in Vienna is awaiting an agreement before voting on a new "red crystal" symbol that would allow Israel to join the movement.
Israel has been denied entry because it does not use an approved symbol.
The Magen David Adom - or Red Shield of David - is not recognised by the Geneva Conventions.
Relief workers and ambulances bearing the symbols of the Red Cross and Red Crescent are protected under international law.
The new "crystal" - a hollow red diamond on a white background - is regarded as being free from religious, national or cultural connotations.
Israel has said it is ready to use it for missions outside the country's borders - as set down by the Geneva Conventions.
Syria is prepared to approve the Red Crystal, but wants Israel to allow the Syrian Red Crescent access to the Golan Heights.
Israel seized the plateau in south-western Syria in the closing stages of the 1967 Six-Day War.
The head of the Syrian Red Crescent, Abd al-Rahman al-Attar, said they had also requested a hospital be built in the area and ambulances provided.
Syrian Minister of State Bashar al-Shaar told reporters that his government's demands were legitimate and legal and must be heard.
"Our people suffer terribly through lack of medical services," he said.
The Syrian demand comes after the Magen David Adom and the Palestine Red Crescent agreed to mutual recognition.
The accord also makes it easier for the Palestine Red Crescent to operate in areas under Israeli control.
Israel's ambassador to the UN in Geneva, Itzhak Levanon, has ruled out letting Syria have similar access.
"The Syrian Red Crescent cannot operate there," Mr Levanon told the BBC earlier this week.
"We have no diplomatic relations with Syria, the issue is simply not in the debate," he added.
The chairman of the conference, Swiss Permanent Representative in Geneva Blaise Godet, said more work had to be done.
"It's going to be a long day," he said.
The BBC's correspondent in Geneva, Imogen Foulkes, says the world's best-known humanitarian movement is being divided by the world's most intractable conflict.