Mr Rouhani succeeded Mahmoud Ahmadinejad, after winning just over 50% of the vote in Iran's presidential election, avoiding the need for a run-off.
Unity was a big theme in Mr Rouhani's inauguration speech to parliament on 4 August, in which he said he would represent all Iranians.
Here, people in Iran reflect on his first 100 days in charge and give their verdict on his achievements so far.
Leila (female), 32, management consultant, Tehran
I'm happy with this president. He doesn't embarrass me as an Iranian. In fact, he gives me some hope. He is politically savvy and smart.
He may not have done anything ground breaking yet, but he has not contradicted himself, nor has anyone higher up contradicted him.
Bread and meat is still expensive, but two things have changed. Firstly, hope has given a boost to investor confidence. Secondly, social pressures are less. You can finally breathe in Tehran.
To some extent he has started to deliver on his domestic political reforms - such as freeing some political prisoners and on foreign policy, with his charm offensive in his UN speech and telephone conversation with President Obama.
He's on the right track - especially on foreign policy. He now needs to engage intimately and openly with Saudi Arabia.
He also needs to reverse the brain drain and invite educated Iranians to return to Iran to help build the economy.
He needs to reverse the deep corruption and moral decline that Mahmoud Ahmadinejad planted in Iranian ethos.
Iran has seen a disgusting moral decay in the past eight years and it will take generations to fix it. But, so far, so good.
Akbar (male), 60s, estate agent, Tehran
After 100 days of this presidency, there has been little concrete achievement.
There is a lot of blaming everything on the last administration, and saying that they left us with a hopeless situation.
President Rouhani has given us words and more words, comforting thoughts and promises. But the real question is - what comes next after that?
Reforms are on hold, it seems. Runaway inflation persists, as do outrageous hikes in rental prices.
Mr Rouhani is carrying high hopes from Washington. But can he deliver? There is a long trek ahead, and he's going at a snail's pace so far.
He is also recruiting heavily from the expediency council - which is mostly made up of retirees and is seen as a cushy number. They also have no clout.
So, there is a lot more that needs to be done.
Nikta (female), 40, doctor, Hamedan province
I'm satisfied with Mr Rouhani's performance so far because I know he has to struggle every day with the troubles forced upon him by extremists.
I don't expect him to perform miracles immediately.
I'm satisfied with the changes he has made in government, such as selecting ministers.
The judiciary system, which is almost always responsible for cruelty and injustice in Iran, is not controlled by the president, but rather the Supreme Leader, so there's not much he can change there.
Our freedom has surely improved, while the economic conditions haven't got any better because our economic situation, mainly at this point, depends on our foreign policy and imposed economic sanctions on Iran.
Mr Rouhani does consider our national interests and the most important job he must do, in my opinion, is establishing a good relationship between Iran and America and other Western countries.
Afshin (male), late 50s, writer, Iran
There have been no surprises in these 100 days. Rouhani is nothing but a puppet chosen by the Supreme Leader Ayatollah Khamenei.
Nothing has changed. In fact, things are now worse. There is more unemployment, more hunger and inflation is at 45 per cent.
My young unemployed friends sleep hungry at night hoping they don't wake up.
The regime is not only fooling the Iranian people, but is also fooling the international community.
There have been no reforms. The regime is executing political prisoners on a daily basis.
Standards of living or freedoms have only improved for the elite and the regime.
Masoud (male), 28, science researcher, Isfahan
I am pleased to say that the economic situation in our country has improved.
I hope that it will now be allowed to flourish in the near future.
To achieve this, we will need to strengthen our relationship with Western countries.
I think President Rouhani should concentrate on solving our problems with the US, because we have the potential to be the most powerful country in the Middle East.
In addition, it's worth mentioning some of the changes he has tried to make, like his attempt to release some political prisoners from jail and allowing the media to express their views about current issues more freely.