LONDON, June 19 (Reuters) - British Prime Minister Theresa May is leading the country through "incredibly challenging times," her spokeswoman said on Monday when asked about media speculation that May might face a challenge from within her Conservative Party.

"These are incredibly challenging times, with a couple of terrible incidents in a week, and she is leading the country through those incidents and through this difficult time," the spokeswoman told reporters.

She had been asked whether May was confident she was still the right person to lead the country.

The Sunday Telegraph, citing senior Conservative sources, said May would face an immediate leadership challenge from eurosceptic lawmakers in her party if she seeks to water down her plans for Brexit.

Britain has been hit by multiple attacks by extremists and by a devastating fire at a tower block in London that killed 79 people. May's authority was severely weakened when she lost her parliamentary majority in an election on June 8.

(Reporting by William James; Writing by William Schomberg; Editing by Estelle Shirbon) ((william.schomberg@thomsonreuters.com; +44 207 542 7778; Reuters Messaging: william.schomberg.reuters.com@reuters.net))