European markets witnessed mixed trade in the opening minutes amid growing fears that the US budget stalemate will continue for some time, potentially hindering efforts to raise the US government's borrowing limit.
The Stoxx Europe 600 index opened 0.1% lower to 309.19.
Britain's FTSE 100 and Germany's DAX 30 opened 0.1% lower.
France's CAC 40 opened 0.1% higher.
Italy's FTSE MIB was trading 0.41% higher.
Spain's IBEX 35 was trading 0.09% lower.
The world's largest economy will run out of cash to pay its bills on 17 October if the government's borrowing limit is not raised. The country's laws limit its borrowing to $16.7tn (£10.3tn, €12.3tn). Market analysts say that the Treasury would probably not be able to pay its bills from October onwards.
Christine Lagarde, the IMF's managing director, warned on 3 October that a failure to raise the US debt ceiling would result in "a fresh setback for a global economy that would take at least a decade to recover from the slump of 2008-09".
"So it is 'mission-critical' that this be resolved as soon as possible," she added.
Earlier, Mario Draghi, the president of the European Central Bank, also warned of the risks from an extended government shutdown.
Among other things, the partial shutdown has hit the flow of economic data from government agencies.
The US Labor Department will not release its crucial nonfarm payrolls numbers on 4 October - the data, which helps gauge the health of the US economy, is a key input for the US Federal Reserve's monetary stimulus decision. The Fed's FOMC meets on 29-30 October.
Market participants in Europe will be tracking political developments in Italy during the day, where the Senate is due to vote on whether to oust convicted politician Silvio Berlusconi from parliament and politics.
Earlier in Italy, Prime Minister Enrico Letta won a confidence vote in the Italian Senate after Berlusconi made an abrupt u-turn and announced he would support the government.
Letta won the vote that kept afloat his five-month old coalition by 236 to 70. The vote was triggered by Berlusconi's decision to pull his five ministers from the coalition government triggering a political crisis.
In Asia and the US
In Asia, the Japanese Nikkei finished 0.94% lower on 4 October. Australia's S&P/ASX closed 0.51% lower while South Korea's Kospi ended 0.12% lower.
Financial markets in China will remain closed till 7 October for the Golden Week holidays.
Earlier in Asia, markets outside India traded lower amid the US government shutdown, which entered its fourth day and threatens to cause serious damage to the world's leading economy.
The partial shutdown of the US government would cost the country anywhere from $300m a day to $10bn in a week in lost economic output, according to economic consultancies and the White House.
According to IHS, which puts the daily loss at $300m, a tiny fraction of America's gigantic $15.7tn (£9.7tn, €11.6tn) economy, a prolonged shutdown could badly hit the US economy as it can put the brakes on consumer and business spending.
The shutdown has also forced President Barack Obama to cancel his Asia trip, which included two key meetings in Indonesia and Brunei.
Obama was to attend the Asia-Pacific Economic Co-operation (Apec) summit in Indonesia and the East Asia Summit in Brunei.
Secretary of State John Kerry would replace Obama at both conclaves. The development comes after the US President cancelled his trip to Malaysia and the Philippines, owing to the partial shutdown.
On Wall Street, indices ended lower on 3 October as the US government shutdown dragged into a third day and after a shootout outside the Capitol building in Washington.
The Dow finished 136.66 points lower or 0.90% at 14,996.48. The S&P 500 closed 15.21 points lower or 0.90% at 1,678.66, while the Nasdaq ended 40.68 points lower or 1.07% at 3,774.34.
All key S&P sectors ended in the red, pulled down by industrials and utilities.