"Our country" would be "我国". They used "国家", which is the term used for one or multiple countries in general. They could have meant just one country, but it's not what I believe to be the most likely interpretation.
国家 simply means state or nation and in this context national. 国家尊严 means national dignity. In the US you rarely address one's dignity, honor, or national dignity. You talk about US values, democratic values, respect for the constitution, etc. So to properly convey the meaning and intonation to a US audience, you would try to rephrase that term into "respect for the country" or something along those lines.
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I'd translate it as: "We will continue to uphold respect towards countries." There's no "pride" or "our" in the original.
I've heard multiple people explain that this is standard phrasing in Chinese to refer to China the country, and not "countries in general."
"Our country" would be "我国". They used "国家", which is the term used for one or multiple countries in general. They could have meant just one country, but it's not what I believe to be the most likely interpretation.
国家 simply means state or nation and in this context national. 国家尊严 means national dignity. In the US you rarely address one's dignity, honor, or national dignity. You talk about US values, democratic values, respect for the constitution, etc. So to properly convey the meaning and intonation to a US audience, you would try to rephrase that term into "respect for the country" or something along those lines.