Alonso edged out Lewis Hamilton's McLaren by 0.105 seconds with Nico Rosberg third fastest for Mercedes ahead of Jenson Button's McLaren.
Sebastian Vettel had bettered Alonso in the morning but was half a second behind when the cars fitted the softer tyres in the afternoon.
Michael Schumacher was seventh fastest ahead of Red Bull's Mark Webber.
Alonso, a two-time winner in Monaco, seemed determined to bend the track to his will and hurtled his Ferrari round in one minute and 15.1234 seconds.
At last Sunday's Spanish Grand Prix, he had led for 18 laps but in the closing stages found himself lapped by the Red Bulls and McLarens because of Ferrari's dwindling race pace, especially on the hard tyres.
Alonso was confident he could deliver a consistent challenge in Monaco because this is a track that demands mechanical grip and precise driving rather than aerodynamic efficiency - an area where Adrian Newey's Red Bull excels.
"He's magic round here," said Team Lotus reserve Karun Chandhok. "His hands are a blur at the wheel.
Chandhok, who was working for BBC Radio 5 Live as an analyst on Thursday, added: "Fernando is a real street fighter on the ultimate street circuit on the calendar. He is a master of controlled aggression behind the wheel."
Alonso was not able to take part in qualifying in Monaco last year after a heavy crash during practice but he still managed to cross the line in sixth despite starting in the pit lane.
Alonso backs Ferrari restructure"I'm confident with the car," Alonso told BBC Sport.
"I'm happy to push and I'm pushing more and more every lap with no big surprises from the car.
"Monaco is about confidence in the car and having a good set-up which enables you to brake later, to go into the corners quicker and to go closer to the wall with no big risk. At the moment the car is offering me that possibility so I'm happy."
The Spaniard did, however, admit that he was expecting a fight back from Red Bull over the weekend.
"It's only Thursday and we know that on Saturday the pressure will increase," he said.
"Red Bull always test different things on Fridays and then on Saturday they are very strong so I expect them to be competitive in qualifying. This is a very unique venue so anything can happen here."
Alonso's team-mate Felipe Massa also looked lively around Monaco, although the Brazilian's enthusiasm led to several scary moments as he almost sailed his Ferrari into the barriers at the Swimming Pool section and the final corner.
Massa, who lives in the principality, finished 0.6secs behind Alonso in sixth place.
There were no major changes to the McLaren cars that Hamilton and Button raced to second and third last time out in Barcelona.
Hamilton and Button both claimed victory in Monte Carlo in their championship-winning seasons and were bullish about their chances of returning to the top step of the podium on Sunday.
It was Hamilton who led the fight, setting the best overall time in the first and third sectors of the circuit to finish the day as Alonso's closest challenger. Button was 0.325secs slower than the leading Ferrari.
Hamilton said: "It is fantastic, I love this track. I've just been so excited all day.
Racing at Monaco's as good as it gets - Hamilton"I kept it out of trouble and I'm happy with the balance of the car and our high-fuel run. It is going to be close, though, as the Red Bull is fast and the Ferrari looks fast too. But I'm pushing and pushing, I want to win this grand prix."
Vettel had set the fastest time in the morning, bettering Alonso by 0.113secs, but finished the later session fifth fastest.
The world champion is targeting his first win in Monaco but often chooses not to show his hand until qualifying and he appeared to spend much of second practice focusing on longer runs on the track.
Webber took a pole-to-flag win in Monaco last season but his running was hampered by an electrical issue with his gearbox and only intermittent use of his power-boost Kers system.
The Australian, who snatched pole from Vettel in Barcelona, was cut adrift from the leading contenders and a worrying 1.5secs off the pace.
Mercedes underlined their ability over one lap with Rosberg third fastest and Schumacher, who took his car sideways into the tyre wall at St Devote in first practice, a second shy of Vettel's benchmark.
The question for the German team will be whether they can produce consistent pace in qualifying and then over 78 racing laps.
"We have a real fight on for pole as Ferrari, McLaren and Red Bull all look very competitive as does Nico Rosberg's Mercedes," added Chandhok.
"The emphasis this weekend has suddenly gone back towards qualifying and we could see six guys fighting it out for pole position."
It was a busy day throughout the field around Monte Carlo's winding streets and bunching traffic led to rising frustrations and mistakes, particularly at the first corner.
Adrian Sutil was even told by his Force India's team radio to "hold it together" as he vented his frustration.
His Scottish team-mate Paul di Resta had to retire from the session with a gear selection problem after setting the 15th fastest time.
The drivers had another problem to literally get to grips with as Pirelli threw another curveball into the mix by introducing the 'supersoft' tyres for the first time this season, with the softs acting as the more resilient 'prime' tyres.
There was generally a positive reaction to the supersofts but Alonso said it was too early to judge whether they would undermine Pirelli's hopes for just a two-stop race by degrading quickly.
Highlights - Monaco GP first practice
