STC, Saudi Arabia's largest telecom company, became Telefonica's largest shareholder in September, building a stake worth 2.1 billion euros ($2.23 billion) through shares and convertible financial instruments.

Acting Economy Minister Nadia Calvino has said Madrid will carry out a thorough evaluation before approving STC's stake, while acting labour minister Yolanda Diaz has called for the transaction to be blocked.

Because Telefonica is considered a defence service provider and a strategic company, the Spanish government has a say in acquisitions and holdings between 5% and 10%.

Spain's SEPI said in a stock market filing on Tuesday that it was carrying out an "exploratory internal analysis over a potential acquisition" of a stake in Telefonica.

The analysis did not imply any decision on an acquisition, SEPI President Belen Gualda Gonzalez said.

STC declined to comment on any potential plans by SEPI.

Major shareholders in Telefonica welcomed STC's investment and ruled out increasing their own stakes.

BBVA Chief Executive Onur Genc said on Tuesday the Spanish bank, which is a leading Telefonica shareholder, had no plans to raise its current 4.87% stake.

"It's a financial stake for us, not a strategic stake. It's a stake (held as) available for sale in the accounting books and we are not looking to increase our shares at all," Genc said.

He would not comment on any potential acquisition by the Spanish state, beyond saying that "from a financial perspective, it is great that investors are showing interest in a company of such importance of Telefonica".

Caixabank, which owns 3.5% stake of Telefonica, said last week it would not raise its stake in response to STC's move, and would analyse with Telefonica any potential cooperation with the Saudi Arabian telecoms company.

($1 = 0.9426 euros)

(Reporting by Inti Landauro and Jesús Aguado; Editing by Pietro Lombardi, Louise Heavens and Alexander Smith)