It comes after leaders of EU institutions condemned Sunday's Venezuelan vote for a constituent assembly, which will write a new constitution and give the ruling party greater powers.
In a statement, the EU's diplomatic service and the European Commission said the bloc had serious doubts about the outcome, and denounced the excessive and disproportionate use of force.
Tajani has now written to Commission President Jean-Claude Juncker and Council President Donald Tusk, demanding asset freezes and travel bans on Venezuelan leaders.
The letter from the Italian MEP said, "The unjustified and arbitrary arrests early this morning of Antonio Ledezma and Leopoldo Lopez, two opposition leaders, is another step towards dictatorship in Venezuela."
He went on, "The constant violation of human rights, the brutal repression exerted by the government cannot continue.
"The EU needs to stand for its values of democracy and freedom of expression also outside of its borders and make its voice heard. We need to show support for the suffering people of Venezuela and take action against the government of President Nicolás Maduro," concluded Tajani.
His comments come after Venezuela's Supreme Court sent two opposition leaders back to prison for allegedly violating the terms of their house arrest and UN Secretary General António Guterres called for urgent political negotiations between the government and the opposition on Tuesday.
Meanwhile, Spain has come out against sanctions, despite the fact Esteban González Pons, a senior MEP from the government's ruling party, called for the EU to impose restrictions on Nicolás Maduro's government.
"Given this situation, it is urgent that the European Union immediately adopt all available measures to try [to get] the Venezuelan government to stop this escalation that only leads to more violence and more division in the country," Pons said.
On Tuesday, a spokesperson's statement on the election to a constituent assembly in Venezuela was released by the Commission.
It read, "The events of the past 24 hours have reinforced the European Union's preoccupation for the fate of democracy in Venezuela.
"The European Union deeply regrets the violence and unrest during yesterday's election. It expresses condolences and its sympathy to the families and friends of all those killed. All sides must refrain from violence.
"The EU condemns the excessive and disproportionate use of force by security forces. The government of Venezuela has a responsibility to ensure respect for the rule of law and fundamental rights, such as freedom of expression and the right to peacefully demonstrate."
It went on, "Venezuela has democratically elected and legitimate institutions whose role is to work together and to find a negotiated solution to the current crisis. A constituent assembly, elected under doubtful and often violent circumstances cannot be part of the solution. It has increased division and will further de-legitimise Venezuela's democratically elected institutions.
"The President and the government have a special responsibility to restore the spirit of the constitution and to re-establish the trust lost by their attempt to set up divisive parallel institutions.
"The fate of democracy in Venezuela is a legitimate concern to all countries in the region, and to Venezuela's partners across the world. In support of ongoing regional mediation efforts, the EU will continue to seek urgent relief for the people of Venezuela and promote a political solution to the crisis."