* Euro zone periphery govt bond yields tmsnrt.rs/2ii2Bqr
By Dhara Ranasinghe
LONDON, Oct 9 (Reuters) - Spanish borrowing costs fell to a one-week low on Monday, narrowing the gap over top-rated Germany, on hopes that Catalonia would this week take a step back from a unilateral declaration of independence from Spain.
Bigger-than-expected demonstrations in Barcelona on Sunday called for Catalonia to remain part of Spain, raising pressure on the regional government to back away from a declaration as soon as Tuesday this week.
The Catalan region's head of foreign affairs, Raul Romeva, told the BBC on Friday that the Catalan parliament intended to make a decision on independence, without specifying when.
The region's pro-independence leader Carles Puigdemont is expected to address Catalonia's assembly at 1600 GMT on Tuesday.
Madrid on Friday meanwhile apologised for the first time for police use of violence in trying to hinder a weekend referendum it had declared illegal, soothing financial market jitters.
"Some of the uncertainty has been reduced -- the tone from Puigdemont has become more conciliatory and (Spain's Prime Minister Mariano) Rajoy has also stepped back," said Peter Chatwell, head of euro rates strategy at Mizuho.
"It is expected that Puigdemont will on Tuesday will say an independence bid in the future will be considered, which is a dramatic step back from expectation last week that a deceleration of independence is imminent."
Moves by local companies to re-locate their headquarters elsewhere are also putting pressure on Puigdemont.
Spain's 10-year bond yield slid 8 basis points in early trade to 1.64 percent, its lowest level in a week.
That narrowed the gap over Germany's 10-year bond yield to 121 basis points -- its tightest in almost a week.
Spanish stocks jumped 1 percent, out performing broader European share markets.
There was also some relief after DBRS ratings agency late on Friday confirmed Spain's rating at A (low).
The ratings agency said Catalonia's bid for independence has increased political tension in the past few months, but several strengths such as a large and diversified economy helped to underpin Spain's credit rating.
The fall in Spanish bond yields dragged down Portuguese and Italian yields , while most other bond yields in the euro area were slightly lower on the day.
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Reporting by Dhara Ranasinghe; Editing by Toby Chopra