The Red Cross said that 10,000 people were trying to flee the main island, Guadalcanal, where native people have attacked immigrants from the outlying islands.
The government of the South Pacific nation has appealed to the self- styled Guadalcanal Liberation Army (GLA) to lay down its arms and has asked for police support from Australia and New Zealand. The Commonwealth Secretariat in London said it had been asked for assistance by Bartholomew Ulufa'alu, the Prime Minister, and was sending Sitiveni Rabuka, former prime minister of Fiji, to visit the islands.
The trouble centres on people from the island of Malaita, many of whom have migrated to the capital, Honiara, which is on Guadalcanal. Malaitans, who include the prime minister, dominate the government, civil service and business.
Guadalcanal people complain of rising crime caused by the newcomers, whom they accuse of squatting on traditional homeland. Last weekend GLA militants drove Malaitans out of villages near Honiara.
This week the island's police commissioner, Frank Short, said that the violence had been localised and he was confident it would soon be brought under control.
Three Malaitans were killed last Saturday when squatters on a palm-oil plantation east of the capital were attacked by GLA militants.
Islanders have taken to setting up illegal roadblocks and Malaitans have responded by blocking roads in to Honiara amid rumours that it was soon to be attacked.
Nick Hurley, the New Zealand High Commissioner to the Solomons, said yesterday that an uneasy calm had returned to the city despite the growing numbers of internally displaced people.
His government had sent tarpaulins to shelter the refugees. The foreign ministries of New Zealand and Australia have advised travellers to avoid the islands.
Yesterday the government offered to pay Guadalcanal landowners $1.7m (pounds 1m) in compensation the loss of their property, on condition that the militants of the GLA came forward to surrender their arms.
In a message broadcast earlier in the week on the Solomon Islands Broadcasting Corporation, the GLA leader, Joseph Sangau, promised to surrender in return for a full amnesty for his supporters.
But Mr Ulufa'alu insisted yesterday that no such amnesty would be granted.