* Spanish, Portuguese bond yields down 13 bps this week
* Biggest falls since July, Sep 2017
* ECB gives up on bigger bond buys but stays cautious
* U.S. jobs data coming up
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Adds graphic)
LONDON, March 9 (Reuters) - Borrowing costs in Spain and Portugal were on track for their biggest weekly falls in more than five months on Friday, a day after the ECB gave up a pledge to increase bond buys if needed but signalled a slow route out of exiting its massive stimulus.
Most bond yields across the single currency bloc were 1-2 basis points higher in early trade, reflecting some market caution ahead of closely-watched U.S. monthly jobs data due later in the day.
But they remained close to lows struck on Thursday after the European Central Bank took just a small step towards weaning the euro zone economy off protracted stimulus by dropping its easing bias.
Having revived euro zone growth with lavish stimulus, the ECB has been dialling back support in tiny increments, fearing that any big change could unravel its work and force an embarrassing and economically damaging policy reversal.
It's that cautious stance that brought comfort to bond investors, especially in southern Europe, a big beneficiary of the ECB's 2.55 trillion euro ($3.16 trillion) stimulus scheme.
"The ECB gave a reassuring message that QE would not come to a swift end in September and stated that the discussion on rate hikes and their timing had just started," said Commerzbank rates strategist Rainer Guntermann.
"This sent relief across the board, particularly for the periphery. It also mostly shut down expectations by some that early 2019 rate hikes were in the cards."
Spain's 10-year bond yield, just marginally higher at 1.41 percent, was set to end the week down around 13 bps -- its biggest weekly fall since July last year.
Portuguese bond yields, hovering close to Thursday's six-week low around 1.79 percent, was set for its biggest weekly fall since September, of around 13 bps.
That left the gap between southern European bond yields and their top-rated peers tighter once more.
The gap between 10-year Italian and German bond yields was at 135 basis points, close to lows hit in the previous session.
Analysts said reports that Italy's centre-right alliance was reaching out to lawmakers from the Democratic Party to seek support for a broad governing alliance after Sunday's inconclusive election was also supporting Italian debt.
U.S. President Donald Trump pressed ahead on Thursday with import tariffs of 25 percent on steel and 10 percent for aluminium.
News that he is also prepared to meet North Korea's Kim Jong Un in what would be the first face-to-face encounter between the two countries' leaders helped ease fears about tensions in the Korean peninsula, denting safe-haven bonds.
Germany's 10-year bond yield was up 1 bps at 0.64 percent <DE10YT-RR>.
(Reporting by Dhara Ranasinghe and Fanny Potkin Editing by Catherine Evans)