Jeremy Corbyn has appealed for calm after a brick was thrown through the window of the constituency office of Labour leadership challenger Angela Eagle.
The Labour leader said it was "extremely concerning" that Ms Eagle had been the victim of a threatening act and there should be no place for violence in politics.
In a statement, Mr Corbyn said he had also received death threats and urged party members to treat each other with "respect and dignity".
It is extremely concerning that Angela Eagle has been the victim of a threatening act and that other MPs are receiving abuse and threats. As someone who has also received death threats this week and previously, I am calling on all Labour Party members and supporters to act with calm and treat each other with respect and dignity, even where there is disagreement. I utterly condemn any violence or threats, which undermine the democracy within our party and have no place in our politics.
Merseyside Police are investigating a report of criminal damage in Manor Road, Wallasey, where Ms Eagle's office is located.
Merseyside Police and Crime Commissioner Jane Kennedy called it a "cowardly" offence but said it would only make Ms Eagle more determined.
Speaking outside the constituency office in Wallasey, Mrs Kennedy said:
This is going to make her more determined to carry forward the debate, to make her case and then let the Labour Party decide and then, God willing, let the country decide. We will get stronger, we will not be intimidated.
The former Labour MP for Liverpool Broadgreen condemned the actions of those behind the damage and said the ongoing intimidation towards Ms Eagle - some of which is homophobic - would not be tolerated.
This behaviour is completely unacceptable, it doesn't matter what their views are this is not acceptable. If they want to dispute it, come and dispute it and talk and argue - but don't sneak up as a coward does and smash a window and run away like a child does at school. It's disgusting, it makes me so angry.