LONDON (REUTERS) - Firming hopes of United States deal to ensure the country does not default on its debt lifted world shares for a second day on Friday and put the dollar on course for its first weekly rise in five.

Republican lawmakers on Thursday offered a plan that would extend the US government's borrowing authority for several weeks, staving off a default that could otherwise come as soon as Oct 17.

While no deal emerged from a meeting with the Democrats at the White House, the two sides appeared ready to end a political crisis that has shuttered much of the US government for over a week and dented Washington's image worldwide.

Asian markets rallied overnight following on from Wall Street's strongest session since January , and European shares were quick to follow suit as they added 0.3 per cent in early trading to Thursday's 1.7 per cent jump.

The dollar was holding its ground, heading for its first weekly rise since early September, and German government bonds tracked gains by US Treasuries. as debt markets continued to show relief.

One US politician said a deal could be struck as early as Friday and Mr Nick Beecroft, chairman of Saxo Capital Markets, said he expected a short-term agreement which would give the US around six weeks of breathing space by Tuesday at the latest.

"I think when we see an agreement on the debt ceiling we will see the high in US Treasury yields drift down due to relief out of that and the stock market will probably do well," Mr Beecroft said, adding there were other implications for financial markets too.

"I think it lends even more support to what I am beginning to feel, which is that tapering is not going to happen until March. When the data eventually comes through, it will look so subdued that there will be no way the Fed's hurdles (to start stimulus withdrawal) would have been met by December."