Jeremy Corbyn has called for "calm" and "dignity" from Labour members after leadership challenger Angela Eagle's constituency office was vandalised.
Mr Corbyn said that "as someone who has received death threats this week" he condemned the "threatening act" and the other "abuse and threats" MPs faced.
The Labour leader urged members and supporters to "treat each other with respect and dignity".
Ms Eagle said Mr Corbyn needed to "get control of his supporters".
Merseyside Police have confirmed that they are investigating an incident at ex-shadow business secretary Ms Eagle's constituency office in Wallasey, Merseyside following reports of criminal damage to a window.
In a statement on the attack on Ms Eagle's office, Mr Corbyn said: "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."
Speaking about the incident, Ms Eagle said: "This isn't the kinder, gentler politics that we were promised".
She urged the Labour leader "to get control of the people who are supporting him and make certain that this behaviour stops".
Dismissing Mr Corbyn's condemnation of the attack, she added: "They are being done in his name and he needs to get control of the people who are supporting him and make certain that this behaviour stops and stops now.
"It's bullying it has absolutely no place in politics in the UK and it needs to end."
In her bid for the leadership, Ms Eagle has accused Mr Corbyn of failing to connect with Labour voters and said she could provide "strong" leadership to "heal our country in these dangerous times".
Asked how she would differ from Mr Corbyn as leader, she told BBC Radio 4's Today: "I wouldn't be hid in my room, not talking to Labour members."
She also said she would not be calling for Article 50 - which kick starts the formal process for leaving the EU - to be signed straight away.
Ms Eagle - who was among the many shadow cabinet members to resign recently- has already secured the 51 nominations from MPs and MEPs required to stand in a leadership contest.
Owen Smith, MP for Pontypridd and Labour's former work and pensions spokesman, has said he would consider making a rival leadership challenge.
The ruling NEC is in the process of deciding whether Mr Corbyn has an automatic right to run in any contest as Labour's sitting leader - or whether he, too, needs 51 nominations to get on the ballot.
The vote on the leadership ballot rules is to be held in secret, according to a Labour source.
BBC political correspondent Iain Watson said the decision the NEC reaches could have far-reaching consequences.
He said if the Labour leader is required to get 51 nominations in order to stand he could struggle to get on the ballot as only 40 of his party backed him on a motion of no confidence recently.
Labour-commissioned legal analysis states Mr Corbyn needs the nominations - just like any challenger - but unions say, as existing leader, he does not.
The BBC has seen legal advice sent to Unite by solicitors that states: "The rules by which the Labour Party is governed are unambiguous: the leader does not require any signatures to be nominated in a leadership election where there is a potential challenger to the leadership."
The solicitors make clear that legal action will be launched unless Mr Corbyn is automatically on the leadership ballot, and they would halt any leadership election by applying to the High Court for an injunction.
What the Labour rule book says:
ii: Where there is no vacancy nominations may be sought by potential challengers each year prior to the annual session of Party conference. In this case any nomination must be supported by 20% of the combined Commons members of the PLP and members of the EPLP. Nominations not attaining this threshold shall be null and void.
Mr Corbyn, who has never had much support among his party's MPs, was elected as leader overwhelmingly in a vote of Labour members and registered supporters last year.
Unite union general secretary Len McCluskey has warned Labour not to seek a "sordid little fix" to prevent Mr Corbyn defending his leadership.
He said it would be "alien to the concept of natural justice" if the Labour leader was not "automatically on the ballot paper".
The rules were "not ambiguous" and the incumbent "must be able to defend themselves", he said.
He also condemned the vandalism of Ms Eagle's constituency office as "reprehensible".
Mr Corbyn had been due to speak at the Unite union's policy conference in Brighton on Tuesday afternoon, but pulled out as it clashed with the party's NEC meeting.
Meanwhile, a YouGov poll for the Election Data website suggested that of 1,221 trade union members surveyed, 63% thought Mr Corbyn was doing badly as leader, compared with 33% who thought he was doing well.
Some 76% said it was unlikely that Mr Corbyn would ever become prime minister, while 69% said it was unlikely Labour would win the next election while he was leader.
And 38% of trade union members said they would vote for Mr Corbyn in a leadership election compared to 35% that would not, the poll suggested.
Union representatives take up 12 of the NEC seats - about a third of the total.
Deputy leader Tom Watson told a recent parliamentary Labour Party (PLP) meeting that his abandoned peace talks with union leaders earlier this month had failed to close the gap between MPs and pro-Corbyn elements of the party.
He said he had "really, really tried" to "find a way forward for the party between two apparently irreconcilable decisions".
But he added: "Clearly the vast majority of the PLP has already made it clear they wouldn't countenance a settlement that involved Jeremy staying in place."