Turkey voted on Sunday to switch to a presidential system, greatly increasing Erdogan's powers.
EU Commission spokesman Margaritis Schinas said on Tuesday that if Turkish President Recep Tayyip Erdogan moved "from rhetoric to action on the issue of the death penalty (it) would be clear signal that Turkey does not want to be a member of the European family".
Turkey's High Electoral Board made a last-minute decision on Sunday to count ballots that had not been stamped by officials.
Erdogan's margin of victory in the referendum was razor-thin.
The No campaign complained of intimidation, detentions and beatings.
Erdogan earlier congratulated cheering supporters at Ankara's airport for "standing tall" in the face of the "crusader mentality" of the West.
Few in Turkey expect legal challenges to the referendum to lead to a recount, let alone a re-run. We did not succumb. It has been in effect since last year's attempted coup. We were here to thank them for their support and cooperation in this process.
The Turkish government has been widely condemned by Western nations for its repression of opposition figures following a failed military coup previous year. It had been due to expire on 19 April.
Turkey rejected on Tuesday the European Union call for referendum probe.
Addressing supporters in Ankara, Erdogan said the country could hold a referendum on its long-stalled European Union membership bid.
"We can conduct a vote of confidence on this as well".
In a separate interview, Gabriel stated that if Ankara were to bring back the death penalty, the move would be "synonymous with the end of the European dream" and mark the end of decades of negotiations to enter the EU.
"Our concern is not what George or Hans or Helga says". As I said this will come before the parliament and if it is passed from the parliament, I would approve this.
Both Germany and France expressed concern about possible election irregularities and called on Mr Erdogan to engage in dialogue with the opposition.
United States president Donald Trump, meanwhile, ignored the concerns about voting irregularities and congratulated Mr Erdogan on his referendum victory. In addition to discussing Erdoğan's win, the two leaders spoke about the recent US strike against a Syrian air base, which Trump thanked Erdoğan for supporting, and the continuing fight against the Islamic State (ISIS).
The voters also turned Turkey's parliamentary system into a presidential one.
Turkey's prime minister on Tuesday called on the opposition to respect the result of a referendum that will give sweeping new powers to the office of the president.
A large number of executive decrees hinge on the state of emergency, including those that facilitated purges of the civil service and the imprisonment of tens of thousands of alleged Gulen supporters.
The new system takes effect at the next election, now slated for November 2019.