In unprecedented dual speeches by two world leaders to Congress, King Hussein and Mr Rabin both pushed for a broad Middle East peace after years of hostility.
'We want normality and humanity to become the prevailing order,' King Hussein said. 'What we are witnessing today, God willing, is a progression from a state of war to a state of peace.'
A day after signing an accord to end the 46-year state of hostility with Israel, King Hussein said the prospects for peace and security 'are growing before our eyes'.
In his spech Mr Rabin said: 'We have come from Jerusalem to Washington because it is we who must say and we are here to say this is our goal: it's peace we desire.'
Mr Rabin said he carried good memories of the two countries' former good relations, but added: 'Walls of hostilities have been built on the River Jordan which runs between us . . . You in Amman and we in Jerusalem must bring down those barriers and walls.'
Launching a new era of peaceful relations at White House ceremonies on Monday, the two leaders signed documents making it possible for their citizens to talk by telephone, fly over one another's territory and co-operate on fighting crime.
Mr Rabin hailed the accord as 'the closest thing to a treaty of peace'.
Both leaders spoke enthusiastically of prospects for normal relations, while acknowledging some thorny issues remain, including conflict over Palestinian refugees in Jordan, sharing of scarce water resources and determining a permanent border.
The agreement calls for cooperation between Israeli and Jordanian police on fighting crime and drug smuggling. Jordan also pledged to work to end the Arab embargo against companies that do business with Israel, but held off from breaking ranks with other Arab states.