The recent global outbreak of the coronavirus disease (COVID-19) has spread to all corners of the globe. The international travel ban, panic buying, and the need for self-quarantine are among the many other social challenges brought about in this new era. Twitter platforms have been used in various public health studies to identify public opinion about an event at the local and global scale. To understand the public concerns and responses to the pandemic, a system that can leverage machine learning techniques to filter out irrelevant tweets and identify the important topics of discussion on social media platforms like Twitter is needed. In this study, we constructed a system to identify the relevant tweets related to the COVID-19 pandemic throughout January 1st, 2020 to April 30th, 2020, and explored topic modeling to identify the most discussed topics and themes during this period in our data set. Additionally, we analyzed the temporal changes in the topics with respect to the events that occurred during this pandemic. We found out that eight topics were sufficient to identify the themes in our corpus. These topics depicted a temporal trend. The dominant topics vary over time and align with the events related to the COVID-19 pandemic.