The BBC's David Willis: The two countries are keen to bury their many differences and to help each other

They also discussed Malaysia's need to raise funds in Singapore to ease its financial crisis.

The unexpected meeting was proposed by Dr Mahathir and follows months of discord over such issues as airspace and border controls.

Dr Mahathir said airspace restrictions would be eased and moves were afoot to resolve the sensitive issue of sharing water.

Malaysia supplies about half of Singapore's water under two treaties which are due to expire by the middle of next century.

'Narrow the differences'

"We talked about how we can improve relations with each other," Dr Mahathir told a news conference after their talks.

The prime ministers summarise the results of their talks

He said the two leaders agreed their officials would curb the heated attacks on each other.

"The two of us will not say anything," he said.

Mr Goh said problems would remain: "But the main thing is to narrow the differences."

He left for Singapore soon after lunch with Dr Mahathir.

BBC Asia affairs analyst Angie Knox believes the reason behind Malaysia's sudden change of heart is both economic and political.

Malaysia is facing its worst-ever recession and needs Singapore's open markets to raise capital for its spending plans.