The UCU said it would consult members on employers' latest proposals this week.
The action, over pay and working conditions, as well as pensions, will affect 150 UK universities.
The University and Colleges Employers Association (UCEA) said the renewed mandate threatened future negotiations.
UCU members voted 85.6% for strike action to continue over pay and working conditions, with a turnout of 56.4%.
In the pensions ballot, 89% voted for strikes to continue with a turnout of 58.4%.
The ballot results mean the union is able to call further strike action, should university staff decide it is required.
The strikes have involved not just academic staff, but those working in universities in other roles.
The UCU had announced 18 days of industrial action during February and March, but called off some of those dates after making "significant progress across a range of issues".
A revised offer was then made by employers, but the union ultimately decided not to consult on it formally with its members.
UCU general secretary Jo Grady said university staff were "in the driving seat" after the latest ballot results, adding that "this dispute is not over".
In response, UCEA chief executive Raj Jethwa hinted at the progress already made in the negotiations, but said the threat of further action "puts these talks in jeopardy".
Unions were offered an improved pay deal for 2023-24 worth between 5% and 8% in January, but said this was a real-terms "pay cut".
The UCEA said it would begin implementing that 2023-24 pay uplift in March, despite talks stalling without an agreement on pay.
Mr Jethwa said universities had "consistently" reported a "low and isolated" impact of strike action on students.