* Portugal gains investment grade rating from Moody’s

* Portuguese and Italian bonds rally

* Spanish bond yields rise on fiscal worries (Updates prices)

LONDON, Oct 15 (Reuters) - Portuguese and Italian government bond yields fell on Monday, outperforming euro zone peers after Moody’s ratings agency upgraded Portugal by one notch, back to investment grade, and Italy’s budget plans came back into focus.

Moody’s is the last of the big three agencies to lift Portugal from the junk status acquired during the euro zone debt crisis.

It upgraded Portugal to Baa3 from Ba1 after the close of European markets on Friday, citing economic and fiscal improvements.

The move is unlikely to unlock major flows of capital as Portugal is already part of the largest investment grade indexes, but DZ Bank rates strategist Christian Lenk said:

“The upgrade is still a positive point. Even though it is not surprising, it may make investors have a second look at Portuguese government bonds.”

Ten-year bond yields dipped briefly below 2 percent before pulling back to slightly over, down two bps on the day.

Italy’s 10-year bond yield was also down two bps on the day at 3.56 percent after the cabinet delayed approval of Italy’s 2019 budget by one day to Tuesday.

Despite apparent broad agreement, government sources said there were tensions between the ruling parties over plans for a partial tax amnesty.

“I don’t think the numbers are credible and the targets won’t be met, but the biggest sell-off in Italy is behind us,” said Nordea Chief Analyst Jan von Gerich.

In contrast to Portugal and Italy, Spain’s 10-year bond yield hit fresh one-year highs at 1.706 percent, though it was set to close only marginally higher at 1.69 percent.

Spain’s Socialists, who hold a minority in parliament, reached a budget deal on Thursday with anti-austerity party Podemos that includes tax hikes and raising the minimum wage.

“We have started to see many accounts worrying about the fiscal situation of Spain. We have been answering many questions over this weekend, many investors are asking about the implications of the new agreement between Podemos and the Socialists,” said BBVA strategist Jaime Costero Denche.

Elsewhere, yields on higher-rated euro zone bonds dipped as investors moved into less risky assets as U.S.-Saudi tensions and Brexit talks dragged on.

A weekend election in the German state of Bavaria that delivered humiliating results for the parties in Chancellor Angela Merkel’s coalition government may also have helped lift appetite for safe-haven bonds.

Germany’s 10-year bond yield dipped to 0.478 percent , its lowest in almost two weeks, before settling at 0.50 percent towards the close. (Reporting by Virginia Furness Additional reporting by Abhinav Ramnarayan Editing by Dhara Ranasinghe and Kevin Liffey)