European shares rose on Friday on hopes of a deal to break the US budget deadlock, while London was lifted by an impressive stock market debut for Royal Mail.

Frankfurt's DAX 30 rose 0.45 percent to end the day at a record high of 8,724.83 points.

In London, the benchmark FTSE 100 index rose 0.88 percent to 6,487.19 points, while the CAC 40 in Paris edged up 0.04 percent to 4,219.98 points.

Madrid added 0.08 percent and Milan climbed 0.24 percent.

"European markets have largely picked up where they left off yesterday continuing to push higher with the FTSE 100 hitting a two week high as optimism builds about the prospects of a US debt ceiling agreement in the coming days," said CMC Markets Analyst Michael Hewson.

Alpari analyst Craig Erlam said the mooted deal which would raise the US government debt ceiling for six weeks "is far from an ideal resolution, however any deal to avoid hitting it for now will always be well received in the markets."

The European single currency firmed to $1.3541 from $1.3520 in New York on Thursday. The dollar rose to 98.50 yen from 97.33 yen.

Sterling fell to 1.1762 euro and dipped to $1.5934.

The price of gold fell to $1,268.00 an ounce on the London Bullion Market, from $1,298.50 on Thursday.

In London, sentiment was boosted as shares in Britain's Royal Mail surged by more than a third in a impressive stock market debut following its controversial part-privatisation.

Royal Mail shares soared 36 percent to 450 pence at the start of conditional deals by institutional investors on the London Stock Exchange, ahead of full trading next week.

That increased the value of Royal Mail to as much as £4.5 billion ($7.2 billion, 5.3 billion euros).

Asian equities meanwhile rallied on hopes that the United States will avoid a default as President Barack Obama and Republican leaders held their first talks Thursday on resolving a budget impasse that has already shut the government down.

With the federal government just days away from running out of enough cash to pay all of its bills and default on its debt, Republicans proposed late Thursday to extend the US borrowing limit for six weeks in return for an agreement by Obama to negotiate on a budget that would restart federal operations.

The White House said Obama would be open to a short-term debt ceiling hike.

Obama was holding further talks with Republican lawmakers on Friday.

Hong Kong advanced 1.16 percent, Tokyo rose 1.48 percent, Sydney climbed 1.63 percent and Shanghai leapt 1.70 percent in value.

Jack Ablin, chief investment officer at BMO Private Bank, said the developments suggest "both sides appreciate the gravity of a default".

He added: "It's not worth sending our country into a tailspin over ideological differences. I think investors are breathing a sigh of relief."

US stocks continued to climb higher on Friday after posting sharp gains on Thursday.

In midday trading the Dow Jones Industrial Average was up 0.56 percent to 15,210.30 points.

The broad-based S&P 500 also rose 0.56 percent to 1,702.07 points, while the tech-rich Nasdaq Composite Index climbed 0.62 percent to 3,784.16 points.