The production and export of cars by foreign automakers is a key driver of economic growth in Hungary, where wages for skilled workers are well below Western European levels.
The car sector employs over 100,000 people and accounts for about a third of industrial output in Hungary, an eastern member of the European Union. Neighbouring Slovakia and the Czech Republic are also major car making hubs in the region.
"Our purpose with today's visit was to place Hungary on the map ... as a country, which puts great emphasis on the car sector," Szijjarto was quoted as saying after talks on Thursday with Tesla's business development and legal directors.
Szijjarto said Tesla executives responded "very positively" to tax breaks linked to research and development and investments in Hungary, as well as the country's corporate tax rate, which at 9 percent is the lowest in the 28-member EU.
The minister said Hungary aimed to install over 3,000 electric charging points by 2019.
He added that Tesla would build two supercharging stations in Hungary by the end of next year, one in the western town of Gyor, an industrial hub home to German premium car maker Audi, and another in Nagykanizsa in the southwest.
Audi is one of Hungary's biggest exporters and revenue earners and the company describes the Gyor engine plant as the world's largest, supplying more than 30 Volkswagen Group sites.
Other major car makers in Hungary include German rival Daimler, PSA Group's Opel, and Suzuki Motor Corp.
South Korea's SK Innovation said last month it would invest 840.2 billion won ($771.86 million) to build an electric vehicle battery plant in Hungary to meet demand from automakers in Europe.
(Reporting by Gergely Szakacs; editing by Jason Neely)