He said a "series of allegations began in less than a hundred hours" after his government took over and there were "instances" with which the government had nothing to do, "yet these controversies have persisted". He, however, did not specify these "allegations" and controversies.
The former Gujarat Chief Minister said "a big challenge" he was facing in Delhi is to "convey to a select group of people about our intentions and sincerity to bring a positive change in this country" and they are "both within and outside government system".
Writing in a blog, he said "every decision we took has been guided solely by national interest" and expressed the commitment to take India to "greater heights in the years to come". Modi said his "confidence and determination has increased tremendously".
He wrote "67 years of previous governments is nothing compared to 1 month but I do want to say that in the last month, our entire team has devoted every single moment for the welfare of the people."
He said "every new government has something that friends in the media like to call a honeymoon period. Previous governments had the luxury of extending this honeymoon period upto a 100 days and even beyond.
"Not unexpectedly, I dont have any such luxury. Forget 100 days, the series of allegations began in less than a hundred hours", he wrote.
Referring to the series of meetings he had with ministerial colleagues, Chief Ministers and officials, Modi said "I feel there are areas where surely we need to improve."
Refusing to "blame anybody", he said "I surely feel that we need to strengthen systems whereby the right things are communicated to the right people at the right time. Hopefully, things will change then."
While talking about the controversies and allegations, Modi said "when one is working with the sole aim of serving the nation determinately, these things do not matter. That is why I keep working and that is most satisfying."
The Prime Minister said when he took over a month ago, "I kept thinking that I am new to this place and some people believed that I would take at least a year or even two to learn the intricacies of the working of the central government. Fortunately, a month later that thought does not exist any longer in my mind."
He said the "support and affection" of the people has been overwhelming and "this inspires us to work even harder".
Recalling that on this date 39 years ago the Emergency had been imposed in the country, he said it "stands out as one of the darkest periods in our history and is a grim reminder of the dangers associated with subverting freedom of speech, press, expression and silencing opposition.
"Our democracy will not sustain if we cant guarantee freedom of speech and expression.
"Today is also a day to reaffirm our pledge to safeguard these values and at the same time create strong institutions through good governance so that that we never ever see those dark days again."
Happy over the "fruitful" meetings with CMs and detailed presentations with ministers and officials, he said "together we will take India to greater heights. Due to people's affection, collective experience of ministerial colleagues and support from officials, my confidence level rose tremendously."
Modi, who led BJP-led NDA to a landslide victory in Lok Sabha elections, wrote "my confidence and determination has increased tremendously and I credit a substantial part of this to the collective experience and wisdom of my ministerial colleagues and also to my experiences as a four-time Chief Minister.
"The affection of the people and support from officials has also added to this confidence in large measure", he wrote.
The Prime Minister wrote: "once again I salute the people of India for their strong support and good wishes as we complete a month in office. I assure you that we are committed to taking India to greater heights in the years to come."
He noted that over the past few days, he has been meeting ministers and officials from various departments who have been making detailed presentations to him.
"I must share that these presentations have enabled a wonderful exchange of thoughts and ideas and we have come up with excellent roadmaps for the various ministries and departments."
He said he looks forward to working closely with Chief Ministers in the times to come.
"26th of June is an important date for me. It marks the completion of one month of our journey to fulfil the aspirations of the people. This day is also another landmark day when in 1975 I witnessed an important phase that taught me the significance of a vibrant democracy.
"26th June was the day when the Emergency started, having been imposed an evening earlier. As a youngster, I have several memories of those testing times."
* I feel there are areas where surely we need to improve: Prime Minister Narendra Modi on completion of 30 days in office
* Series of allegations began in less than 100 hours but when one is working with sole aim of serving the nation, these things do not matter
* There have been some instances in the last month with which our govt had nothing to do yet these controversies have persisted
* A big challenge I am facing in Delhi is to convey to a select group of people about our sincerity, they are within and outside govt system