The two-day official visit saw Priti Patel meet ministers in Athens before going out on patrol with the Hellenic coastguard off the island of Samos to learn more about the methods used to prevent small boat crossings.
She also visited a newly built migrant reception centre and heard about the country’s asylum reforms, the Home Office said.
According to her department, she discussed Greece’s response to the “scale and threat posed by small boat crossings in the Aegean and the involvement of organised immigration crime gangs in those crossings” with the country’s shipping and island policy minister, Ioannis Plakiotakis, and heard more about its asylum reforms from the migration minister, Notis Mitarachi.
The visit comes three months after immigration minister Chris Philp carried out a similar trip.
Greece is said to have been hardening its approach to migrants in recent months with tougher border controls and walled camps. It has denied accusations its coastguard pushes back migrant boats as they enter Greek waters.
Some campaigners have described the so-called closed and controlled camps as inhumane, raising fears the visit indicates the UK could be considering similar options.
Pictures posted on Mr Mitarachi’s Twitter account show he and Ms Patel looking at diagrams of the centre and the construction.
Home Office officials insisted no talks on sharing such centres with Greece took place and the visit was not to look at using similar methods in the UK.
The visit comes after the UK Government put forward plans for sweeping reforms of the asylum system, which could see migrants turned back at sea and offshore processing centres set up so those seeking refuge are sent abroad while their claims are determined.
The vast majority of asylum seekers arrive by sea in the countries on the EU’s southern and south-eastern borders in Greece, Italy and Spain.
Those countries, along with Malta and Cyprus, have been asking other European countries for help caring for those brought ashore seeking asylum.
Migration Minister Notis Mitarachi was reported in the past as saying: “Our policy is strict but fair”.
Meanwhile, Ms Patel has pledged a new “fair but firm” new plan for immigration, with the Nationality and Borders Bill now being considered by Parliament.
Dubbed the anti-refugee Bill by campaigners critical of the plans, it intends to make it a criminal offence to knowingly arrive in the UK without permission, with tougher sentences for those found doing so and for people smugglers.
Only by working together can we break up these crime gangs that extend throughout Europe and beyond, and stop the horrific trade in people across the continent
It means, for the first time, how someone enters the UK – legally or “illegally” – will affect the progress of their asylum claim and their status in the UK, if their bid is successful.
The Home Office previously said the Government is in discussions with several European countries to strike up deals to return nationals determined to be in the UK illegally. But it is understood so far no agreements have been reached.
The department was unable to confirm whether Ms Patel took part in any such negotiations with her Greek counterparts on this visit.
Ms Patel said: “We have seen a surge in illegal migration across Europe, and we must continue to work closely with Greek partners to tackle this challenge that both our countries face.
“Only by working together can we break up these crime gangs that extend throughout Europe and beyond, and stop the horrific trade in people across the continent.”
During the trip, Ms Patel also met with the minister of citizens’ protection, Michalis Chrisochoidis, and “reaffirmed their commitment to continuing to work together to address the challenges Greece and the UK face from terrorism and organised crime”.