Italy host Malta in Florence on Thursday before travelling to Palermo to host a Bulgarian side desperate to relaunch their qualifying campaign with four games remaining in Group H.
Victory from both games would see Italy book their ticket for the European Championships with two games to spare.
Conte, who led Juventus to three consecutive titles prior to taking over the Italy job, advised his squad to put aside what is going on in domestic competition.
"It's an important week for us. With two wins against Malta and Bulgaria we can qualify for Euro 2016," said Conte, who took over from Cesare Prandelli following Italy's first-round exit from last year's World Cup.
"I want the players to forget what's happening in their various clubs. All we should be focusing on is winning our games.
"We want to win them all and finish top of the group to give our confidence and self-esteem a boost."
Italy are only one point behind group leaders Croatia, who on paper have 14 but were deducted a point following a 1-1 draw with Italy in June after a swastika was scrawled on the pitch before the fixture in Zagreb.
But among Italy's squad, competition for places is tight.
Conte has rejuvenated his squad with players like Simone Zaza, but the striker's move back to Juventus following a successful loan spell at Sassuolo could come at a price if he fails to play regularly.
"I will pay close attention to what's going on and who is playing... if some of the players are not playing then they will be at risk."
While Bulgaria have given Italy plenty of food for thought in past encounters, notably holding them to a 2-2 draw in Sofia last March, Malta are the group's whipping boys.
They are bottom of the pile with one point from six games in which they mostly frustrated their opponents by defending en masse and striking on the counter.
Conte says he wants no slip-ups over the coming two fixtures.
"It's crucial we take the six points, it would allow us to start preparing for June. Malta's squad has grown a lot in the past years, they defend with eight players and they're a tough nut to crack for most teams."
AC Milan midfielder Andrea Bertolacci agreed with Conte's assessment.
"We know we can qualify if we win these two games, so on Thursday and Sunday we'll be lining up looking to rubber stamp it."
Conte added Napoli forward Lorenzo Insigne to his squad after Toronto FC striker Sebastian Giovinco suffered an injury knock.
There is still no room for Liverpool misfit Mario Balotelli, who has returned to AC Milan on loan in a bid to resurrect his career, and in the meantime Brazil-born Eder has laid claim to one of the striker's spots.
Sampdoria striker Eder has hit four goals in two Serie A games so far to top Italy's scoring charts and pledged his loyalty to Conte's cause.
"I don't know if I will start but I'm giving my all every day and I'm here if and when the coach calls on me," he said.