The British Museum is leading calls to stop sites of archaeological interest being destroyed during the conflict in Iraq.
Iraq's heritage "is under threat"
It is worried the war could wipe out thousands of years of the country's history.
Archaeologists and politicians have written to the prime minister asking for a number of sites to be respected during the conflict.
John Curtis from the British Museum said: "The Sumerians, Babylonians and Assyrians all had their homeland in Mesopotamia, which is modern Iraq.
"It is incredibly important. It's not just the cultural heritage of Iraq but the cultural heritage of the world."
The area between the Euphrates and Tigris rivers is often called the cradle of civilization.
Baghdad city museum contains 100,000 artefacts dating from 7,000BC to AD1,000 chronicling the achievements of Sumerian, Babylonian, Assyrian, Persian and Islamic civilizations.
This was Alexander the Great's capital and the place where the Hanging Gardens were built
Seleucia is a site 20 miles south of Baghdad founded by the Greeks and replaced Babylon as the region's commercial centre
Basra Al-Qurna is reputed to be the site of the Garden of Eden complete with a gnarled tree know as Adam's tree
For centuries the people living in the land which is now Iraq led the world in medicine, engineering and even invented writing.
Experts estimate that there are about 100,000 sites of cultural and historical importance in Iraq.
About 10,000 of these have been excavated but thousands more remain untouched.
The Ministry of Defence, in response to a written parliamentary question, said: "In our military planning, very careful attention is applied to ensure that we minimise the risk of damage.
"We are confident that our servicemen and women will respect the rich heritage of the Iraqi people."
The British Museum has said visitor numbers have soared since the conflict.
A spokeswoman said: "It's just general curiosity from what's going on [with the war]," she said.
"Members of the public are coming from all over the world."